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A car travels downhill at 72 km per hr, on the level at 63 km per hr, and uphill at 56 km per hr. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What is the distance between the two towns.

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Posted · Report post

273 km

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Posted (edited) · Report post

273km

Solution:

(40minutes/60minutes) = Conversion to hours

Ratio between the two speeds (uphill:downhill) = 72/56

So, 72/56x - 1x = (40/60)

Or

(72/56-1)x = (40/60)

(40/60)/(72/56-1) = x

x = 2 1/3hrs

Plug and chug to verify

72km per hr for 2 1/3 hours = 168 km

Remaing time of 1 2/3 hours at 63 km = 105

Reverse way:

56 km per hour for a distance of 168 km = 3hours

and the other time was 1 2/3 which equals 4 hours, 40 minutes

Hope my explanation is clear

Edited by PolishNorbi
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Posted · Report post

A car travels downhill at 72 km per hr, on the level at 63 km per hr, and uphill at 56 km per hr. The car takes 4 hours to travel from town A to town B. The return trip takes 4 hours and 40 minutes. What is the distance between the two towns.

Can we assume that the road from A to B has a constant grade?

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Can we assume that the road from A to B has a constant grade?

Bonanova, I think you don't need to assume that A to B have constant grade, but you do need to assume (or maybe its given) that he drives at constant speed of 72kmph downhill, regardless of the gradient and 56kmph uphill regardless of the gradient .

Let's say that there is x km of downhill, y km of level and z km of uphill from A to B and that the car accelerates infinitely between such changes of gradient and that he drives at constant speed of 72kmph downhill, regardless of the gradient and 56kmph uphill regardless of the gradient .

To find: x+y+z = d

Going from A to B: --- (i)

x/72+y/63+z/56 = 4

=> 7x+8y+9z = 2016

Going from B to A: --- (ii)

x/56+y/63+z/72 = 4.67

=> 9x+8y+7z=2352

Adding (i)+(ii)

16(x+y+z) = 4368

Therefor, d = 273 km

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Can we assume that the road from A to B has a constant grade?

You may assume that the car travels at constant speed during the three events. That is, at constant speed of 72 km per hr on the downhill, at 63 km per hr on the level, and at 56 km per hr on the uphill.

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