Problem Solving

PS Question:
A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 min after passing her, while the hiker continues to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?
6 2/3
15
20
25
26 2/3

For this problem, we use the d = r*t formula

Hiker distance after 5 minutes
r = 4 miles / 1 hour -> 4 miles / 60 minutes -> 1 mile / 15 minutes
t = 5 minutes
d = r*t -> 1/15 * 5 = 1/3 miles

Cyclist distance after 5 minutes
r = 20 miles / 1 hour -> 20 miles / 60 minutes -> 1 mile / 3 minutes
t = 5 minutes
d = r*t -> 1/3 * 5 = 5/3 miles

Distance between the two after 5 minutes
5/3 - 1/3 = 4/3 miles

Time it takes Hiker to travel 4/3 miles
4/3 = 1/15 * t
t = 20 minutes

Hey tmmyc,

Why is t=5 and not t for both, with the 5 minutes piece of information added in. Such as t + 5 or t - 5. I just wanted to know. Thanks.

thanks a lot...

AleksandrM wrote:Hey tmmyc,

Why is t=5 and not t for both, with the 5 minutes piece of information added in. Such as t + 5 or t - 5. I just wanted to know. Thanks.

Think about it this way. The hiker is walking at his own pace the cyclist is biking at his own pace. The question states the cyclist passes by the hiker, goes for 5 minutes, then stops to wait for the hiker.

Therefore, we start the clock when the cyclist passes the hiker and stop the clock after 5 minutes. Since the cyclist is going faster than the hiker, there is a certain amount of distance between the two now, which is actually the cyclist's distance traveled minus the hiker's distance traveled in those 5 minutes.

The question is asking how long until the hiker catches up. We can get this by first calculating the distance between the two, and using the hiker's rate, determine the amount of time to travel that distance. Does that make sense?

Yes. Thanks.