A car travels 180 miles in t hours at a speed of r mph. If the car travels half as fast but three times as long, how far does it travel?

Question

Use the fact that distance equals speed times time.

Answer 1

d = vt

 

where:

v = speed

d = distance

t = time

 

Based on the formula, each quantity is directionally proportional to each other.  Since we don't have enough numbers to work with, we will utilize our concept skills.

 

If the car travels half the speed, then the car is slowing down and covers a short distance in a certain amount of time than it did originally.  So we divide the default distance by 2.

 

180 / 2 = 90

 

The new distance so far is 90 miles.

 

But now it takes the car 3 times as long to get to its destination.  The longer it takes, the more distance you will cover.  Multiply the current distance by 3.

 

90 * 3 = 270

 

 

The car travels 270 miles.

Answer 2

180 = t · r

 

d = 3t · r/2

d = 3rt / 2

d = (3/2)rt

d = (3/2)(180)

d = 3(90)

d = 270