# How long did it take Peter to reach Wayne's house from the time he left his own house?Wayne and Peter decided to visit one another and set off at the same time to each other's house. When they...

How long did it take Peter to reach Wayne's house from the time he left his own house?

Wayne and Peter decided to visit one another and set off at the same time to each other's house. When they met on the road joining their houses, they forgot that they wanted to see each other and continued walking. Wayne reached Peter's house 8 minutes after the meeting and Peter got to Wayne's house 18 minutes after the meeting. How long did it take Peter to reach Wayne's house from the time he left his own house?

Let x be the distance from the meeting place to Wayne's house and let y be the distance from the meeting place to Peter's house.

Now speed, time and distance are related by the formula `v=d/t` , which may be rearranged to have time `t=d/v` . If Peter's speed is `v_p` and Wayne's speed is `v_w` , then `v_p=x/18` and `v_w=y/8` .

Now Wayne and Peter both left their houses at the same time, so the time they took to get to the meeting place we will call t. This means that `v_p=y/t` and `v_w=x/t` . These times are equal which gives `y/v_p=x/v_w` .

Substituting for x and y gives the equation `{8v_w}/v_p={18v_p}/v_w` . Rearranging, we find the ratio `v_w^2/v_p^2=9/4` , and then take square roots to get `v_w/v_p=3/2` . This means Wayne walks 1.5 times faster than Peter. So if Wayne took 8 minutes to walk the distance from the meeting place to Peter's house, then Peter will take 12 minutes to cover the same distance. The total time that Peter needs to take to go from his house to Wayne's house is 12 minutes plus the other 18 minutes.

**It takes Peter 30 minutes to go between the houses.**

Let the distance between the houses is x m. Then let us take the distance from peter's home to the point of meeting is y m.

The time peter takes to come to meeting point = t1

The time Wayne takes to come to meeting point = t2

Let take the constant speed of peter is v1 and Wayne is v2.

distance = velocity * time

Peter travels y m from home to meeting point.

y = v1*t1-----(1)

Peter needs 18min to reach Wayne's house after meting

(x-y) = v1*18-----(2)

Wayne travels (x-y)m from home to meeting point.

(x-y) = v2*t2-----(3)

Wayne needs 8min to reach peter's house after meting

y = v2*8----(4)

The answer we want is the time (t) which takes peter to reach Wayne's home.

(1)+(3)

x = v1t1+v2t2-----(5)

(2)+(4)

x = v1*18+v2*8-----(6)

Since (5) = (6)

t1 = 18 and t2 = 8

t = t1+18 = 18+18 = 36

**So it takes 36 min for Peter to reach Wayne's home.**

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