Question

One hour after a hiker left a camp, a cyclist set out to catch up. If the hiker traveled 3 miles per hour and the cyclist traveled 6 miles per hour faster, how long will it take the cyclist to catch up with the hiker?

Answer 1

Given:

(i) The hiker traveled 3 miles per hour.

(ii) The cyclist traveled 6 miles per hour faster

To find:

(i) How long will it take the cyclist to catch up with the hiker.

Solution:

Given, the speed of hiker = 3 mph.

In 1 hour, the hiker would travel a distance equal to (3*1) miles

= 3 miles.

Again, the speed of cyclist is 6mph faster than hiker.

So, speed of cyclist = (6+3) mph

= 9 mph.

Let the cyclist take 't' hours to catch up the hiker.

So, distance travelled by the cyclist in 't' hours = 9t miles.

And the hiker will cover a distance of 3t miles in 't' hours.

Total distance the hiker will cover = 3t + 3.

So, 3t+3 = 9t

⇒ 6t = 3

⇒ t = 3/6 = 0.5 hours.

1 hour = 60 mins.

0.5 hours = 30 mins.

So, the cyclist will take 30 mins to catch the hiker.