power prep 2 and hikers

Hiker- 4m/h
cyclist 20 m /h

from the point where they meet cyclist travelled for 5 min further

so in 5 min

20 --- 60
x------5

60x=100

x=10/6 miles

jiker to cover the distance of

4---- 60
10/6---y

4y=100

y =25 min


Vishu

thanks for the post!

OA is C. I donno how it can be C...
may be the power preb was mistaken....

Forgot to consider ! the five mintues hiker covered whilst cyclist for 5 min




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

4.......>
20.......>

So actually for 5 minutes the distance will be: 5(20-4)

time = (5x16) / 4

time = 20 minutes

Relative speeds come into picture:

V1 == Hiker
V2 == Cyclist

For 5 mins ( 1/12 hours)

Distance between them would be 20-4/1/12
= 4/3

Now to cover 4/3 miles
Hiker will take (4/3)/4

that is 1/3 hours
that is 20 minutes:

ronnie could you please post the formula for relative speed..
thank you.

Brent Hanneson wrote:With this question, it helps to refrain from performing more calculations than are necessary.

The important thing is to recognize that if someone is travelling 5 times faster than me, it will take me 5 times longer to get to the same destination as the person travelling faster.

So, if it takes the cyclist 5 minutes to travel a certain distance, it will take the hiker 5 times as long to travel the same distance.

So, the hiker will take 25 minutes - Answer choice D

Amen to that

- pradeep