SOLUTION: Going to Baguio, Ana and Elsa decided to drive all day. During the first part of the trip on the highway they averaged 60 kph. When they got to Baguio, traffic caused them to avera

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Question 956604: Going to Baguio, Ana and Elsa decided to drive all day. During the first part of the trip on the highway they averaged 60 kph. When they got to Baguio, traffic caused them to average 30 kph. The distance they drove in Baguio was 100 km less than their distance on the highway. What was their total driving distance if they spent 50 minutes more on the highway than they did in Baguio?

Found 3 solutions by josgarithmetic, MathTherapy, Theo:
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website!
_______________________speed_________time___________distance
First Part_____________60_____________(___)__________d-100
Baguio_________________30_____________(___)___________d
Total________________________________50/60

Uniform Travel Rates rule, RT=D for rate time distance.
of an hour is 50 minutes.

_______________________speed_________time______________distance
First Part_____________60____________(d-100)/60__________d-100
Baguio_________________30_____________d/30________________d
Total________________________________5/6

The question is to find total driving distance. Solve the total time
equation for d, the distance done in Baguio:

Compute from that.

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Going to Baguio, Ana and Elsa decided to drive all day. During the first part of the trip on the highway they averaged 60 kph. When they got to Baguio, traffic caused them to average 30 kph. The distance they drove in Baguio was 100 km less than their distance on the highway. What was their total driving distance, if they spent 50 minutes more on the highway than they did in Baguio?

Let distance to Baguio be D
Then distance covered in Baguio is: D � 100
Time spent driving on highway:
Time spent driving in Baguio:
Since 50 mins more was spent driving on highway, then we can say that:

D = 2(D � 100) + 50 ------- Multiplying by LCD, 60
D = 2D � 200 + 50
D � 2D = - 200 + 50
- D = - 150
D, or distance to Baguio = , or 150 km
Distance covered in Baguio: 150 � 100, or 50 km
Total distance traveled: 150 + 50, or km

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
let x equal the distance they traveled at 60 kmph.
let t equal the time they took to travel at 30 kmph.

the general equation is rate * time = distance.

this can be represented by:

r * t = d, where r = rate and t = time and d = distance.

During the first part of the trip on the highway they averaged 60 kph.

r * t = d becomes 60 * t1 = d1

When they got to Baguio, traffic caused them to average 30 kph.

r * t = d becomes 30 * t2 = d2.

The distance they drove in Baguio was 100 km less than their distance on the highway.

d2 = d1 - 100, so the equation in Baguio becomes:

30 * t2 = 100 - d1.

What was their total driving distance if they spent 50 minutes more on the highway than they did in Baguio?

50 minutes is equal to 50/60 hours, which is equal to 5/6 hours.

t1 = t2 + 5/6 hours, so the equation on the highway becomes:

60 * (t2 + 5/6) = d1

you have two equations that need to be solved simultaneously.

they are:

60 * (t2 + 50/60) = d1

30 * t2 = d1 - 100

one way to solve these is to set both equations equal to d1 and then solve for t2.

we'll do it that way.

in the second equation, add 100 to both sides of the equation to get:

30 * t2 + 100 = d1

now both equations are equal to d1.

you have:

60 * (t2 + 5/6) = d1

and you have:

30 * t2 + 100 = d1

replace d1 in the first equation with 30 * t2 + 100 from the second equation to get:

60 * (t2 + 5/6) = 30 * t2 + 100

simplify to get:

60 * t2 + 60 * 5 / 6 = 30 * t2 + 100

simplify to get:

60 * t2 + 50 = 30 * t2 + 100

subtract 30 * t2 from both sides of this equation and subtract 50 from both sides of this equation to get:

60 * t2 - 30 * t2 = 100 - 50

simplify to get:

30 * t2 = 50

divide both sides of this equation by 50 to get:

t2 = 50/30 = 5/3.

now that you know what t2 is, you can solve for d1.

the second equation is:

30 * t2 = d1 - 100

replace t2 with 5/3 to get:

30 * 5/3 = d1 - 100

simplify to get:

50 = d1 - 100

add 100 to both sides of this equation to get:

d1 = 150.

that's your solution.

t2 = 5/3
d1 = 150

d1 represents the distance they traveled on the highway.
d2 represents the distance they traveled in Baguio.
150 + 50 = 200 km.

the total distance they traveled was 200 kilometers.

to see if this makes sense, we'll go back to the original problem statement.

Going to Baguio, Ana and Elsa decided to drive all day. During the first part of the trip on the highway they averaged 60 kph. When they got to Baguio, traffic caused them to average 30 kph. The distance they drove in Baguio was 100 km less than their distance on the highway. What was their total driving distance, if they spent 50 minutes more on the highway than they did in Baguio?

we have figured out that the time they spent traveling in Baguio was 5/3 hours.
we have figured out that the time they spent on the highway was 5/3 + 5/6 hours

5/3 hours * 60 = 100 minutes.

5/3 + 5/6 hours is equal to 15/6 hours * 60 is equal to 150 minutes.

they spent 150 minutes on the highway and they spent 100 minutes in Baguio.
they spent 50 more minutes on the highway than they spent in Baguio.

we have figured out that the distance they traveled on the highway is 150 km.
we have figured out that the distance they traveled in Baguio was 50 km.

this means that the distance they traveled on the highway is 100 kilometers more than the distance they traveled in Baguio.

all the requirement sof the problem have been satisfied, so the solution looks good.

the solution is:

Their total traveling distance was 200 kilometers.