Question

A biker’s speed is 1.5 times faster than a walker’s speed. They start moving simultaneously in the same direction from the same point and, after 1.5 hours, the distance between them is 12.5 miles. What are their speeds?

Answer 1

Answer: Speed of walker and biker will be 16.67 miles per hour and 25 miles per hour respectively.

Explanation:

Let the speed of a walker be x

Let the speed of a biker be 1.5x

They are moving in the same direction,

so, their Relative speed will be

`1.5x-x=0.5x`

Time taken = 1.5 hours

Distance between them = 12.5 miles

As we know the formula for "Distance":

`Distance=Speed* time\\\\12.5=1.5* 0.5x\\\\(12.5)/(1.5)=0.5x\\\\8.33=0.5x\\\\(8.33)/(0.5)=x\\\\16.67\ miles\ per\ hour=x`

Hence, Speed of walker be 16.67 miles per hour

Speed of biker be

`1.5* 16.67=25\ miles\ per\ hour`

Answer 2

Let the walker’s speed be W, then the biker’s is W+1.5W=2.5W. Difference in speed is 1.5W. Distance=speed times time, so 12.5=1.5W×1.5=2.25W, and W=12.5/2.25=1250/225=50/9=5.56 mph. The biker’s speed is 2.5W=125/9=13.89 mph to 2 Dec places.
(Note: “1.5 times faster than a walker’s speed” could not reasonably mean the biker’s speed=1.5W because this would give W=16.67 mph, which is very fast for a runner, let alone a walker (!), and a biker’s speed of 25mph.)