SOLUTION: Kory drives from Edmonton to Lloydminster and back. Going to Lloydminster, he drives with an average speed of 96 km/h. For the return trip, he averages a speed of 100 km/h. The tot

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Question 1199402: Kory drives from Edmonton to Lloydminster and back. Going to Lloydminster, he drives with an average speed of 96 km/h. For the return trip, he averages a speed of 100 km/h. The total time driving is 5.1 hours.
Found 3 solutions by math_tutor2020, greenestamps, josgarithmetic:
Answer by math_tutor2020(3820)   (Show Source): You can put this solution on YOUR website!

Your post seems incomplete.
Are you wanting to know the average speed throughout the whole roundtrip?
If so, then read on.

d = the distance from Edmonton to Lloydminster
This is some positive real number
The distance is in kilometers.

x = time taken to drive from Edmonton to Lloydminster
y = time taken to drive from Lloydminster to Edmonton
The time durations are in hours.

When going to Lloydminster, we have this equation
distance = rate*time
d = 96x
Let's isolate x
x = d/96

The return journey has this equation.
distance = rate*time
d = 100y
y = d/100

The two time durations x and y must add to the total driving time of 5.1 hours.
x+y = 5.1
d/96 + d/100 = 5.1
d/96 + d/100 = 51/10

A common multiple of 96, 100, and 10 is 9600
I simply did 96*100 = 9600

We can multiply both sides of that equation by 9600 to clear out the fractions.
d/96 + d/100 = 51/10
9600*(d/96 + d/100) = 9600*(51/10)
100d + 96d = 48960
196d = 48960
d = 48960/196
d = 249.795918367347
d = 249.795918
This is the approximate distance, in kilometers, from Edmonton to Lloydminster.

The round-trip distance is twice that
2*249.795918 = 499.591836
This assumes Kory travels the same route each way.

To find the average speed throughout the round trip, we will then do the following:
distance = rate*time
rate = distance/time
rate = (499.591836 km)/(5.1 hrs)
rate = 97.959184
rate = 97.96 km per hour
Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!


Since you did not ask a question, I will assume we are supposed to determine the distance between Edmonton and Lloydminster.

The distances are the same, and the ratio of the speeds is 96:100 = 24:25. That means the ratio of the times at the two speeds is 25:24.

That means 25/49 of the total time is spent at the lower speed and 24/49 at the higher speed.

25/49 of the total 5.1 hours is (25/49)(51/10)=1275/490=255/98 hours.

The distance from Edmonton to Lloydminster is (255/98)(96)=249.8km to 1 decimal place.
Answer by josgarithmetic(39632)   (Show Source): You can put this solution on YOUR website!
You did not finish the problem description or did not write what question to answer. You can expect that the
distance is the same value in each direction.
                 SPEED         TIME           DISTANCE

GOING TO            96
COMING BACK        100

TOTAL                           5.1


You might continue:
                 SPEED         TIME           DISTANCE

GOING TO            96         5.1-x          96(5.1-x)
COMING BACK        100          x            100x

TOTAL                           5.1

You should understand that both directions being same length,
.
Solve for the time "coming back", and then evaluate time "going to" and the distance either direction.
-----






----
GOING TO, 2.602 hours, or 2 hours 36 minutes
COMING BACK, 2.498 hours, or 2 hours 30 minutes
DISTANCE BETWEEN THE CITIES, 250 kilometers
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