SOLUTION: time & distance math problem two car run to a place at the speed of 45 km/hrs and 60 km/hrs respectively. if the second car takes 5 hrs less than tha first car for completing the j

Question 658851: time & distance math problem two car run to a place at the speed of 45 km/hrs and 60 km/hrs respectively. if the second car takes 5 hrs less than tha first car for completing the journey, the length of the journey will be
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
r.1 = rate of the first car.
r.2 = rate of the second car.
t.1 = time it takes to go the distance for the first car.
t.2 = time it takes to go the distance for the second car.
t is the overall time.
d is the overall distance.
you are given.
r.1 = 45 km/hr
r.2 = 60 km/hr
you are also given that the second car takes 5 hours less than the first car to travel the same distance.

this means that t.2 = t.1 - 5

the formula used is rate * time = distance or r*t = d.

for the first car this becomes r.1 * t.1 = d
for the second car this becomes r.2 * t.2 = d

since we know that t.2 = t.1 - 5, we can substitute for t.2 in the second equation to get r.2 * (t.1 - 5) = d

our 2 equations are now:
r.1 * t.1 = d
r.2 * (t.1 - 5) = d

since we know the value of r.1 and r.2, e can substitute in each equation to get:

45 * t.1 = d
60 * (t.1 - 5) = d

since both expressions on the left side of each equation are each equal to d, we can set them equal to each other to get:

45 * t.1 = 60 * (t.1 - 5)

we have now reduced the problem to a single equation with one unknown which can be solved for t.1.

simplify the equation to get:
45 * t.1 = 60 * t.1 - 5*60
simplify further to get:
45 * t.1 = 60 * t.1 - 300
add 300 to both sides of this equation and subtract 45 * t.1 from both sides of this equation to get:
300 = 60 * t.1 - 45 * t.1
factor out the t.1 in the right side of the equation to get:
300 = (60 - 45) * t.1
simplify to get:
300 = 15 * t.1
divide both sides of the equation by 15 to get:
300/15 = t.1 which results in t.1 = 20 hours.

you can now solve for t.2.

since t.2 = t.1 - 5, this means that t.1 = 15

you have t.1 = 20 hours and t.2 = 15 hours.

you can now solve for d.

rate * time = distance.

r.1 * t.1 = d
r.2 * t.2 = d

substitute known values for t.1 and t.2 and r.1 and r.2 and you get:

45 * 20 = d
60 * 15 = d

both equations should give the same value for d.

45 * 20 = 900
60 * 15 = 900

d = 900 kilometers.

first car travels at 45 km/hr for 20 hrs for a distance of 45*20 = 900 km.
second car travels at 60 km/hr for 15 hrs for a distance of 60*15 = 900 km.

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