# math

posted by vincent

A boy travels on his bicycle at the rate of 6 miles per hour and his sister on hers
at the rate of 5 miles per hour. They start at the same time and place and travel over the same road in the same direction. After traveling for 3 hours, the boy turns back. How far from the starting point has his sister traveled when they meet?

1. Ms. Sue

You've posted many math questions in the last couple of days. Most have been answered.

2. leena

i can help u.

First, draw a picture (it helps to visualize ^_^):

S　　　　a　　　　M　　　　b　　　　T
where S = start
M = meeting point
T = turn around point
Let b = brother and a = sister

The formula is Distance = Rate x Time

First focus first on the brother:
D = RT, where R = 6mph and T = 3
D = 6 x 3 = 18 miles before turning back

S　　　　　　　　M　　　　　　　　T
---------------------------18 miles --------------->b

Now focus on the sister
D = RT, where R = 5mph and T = 3
D = 5 x 3 = 15 miles

S　　　　　　　　　　　　　　M　　T
-------------------15 miles------>a　　　　　b
<---- 3 ---->
The difference in their distance is now 3 miles apart.

Now the question changes, the brother is heading towards his sister at 6mph and the sister is heading towards her brother at 5mph, with a distance of 3 miles between them

For the brother
(6)(t) = D1
For the sister
5(t) = D2

Find t when D1 + D2 = 3
(6)(t)+ (5)(t) = 3
6t + 5t = 3
11t = 3
t = 3/11

So the time the sister meets with her brother is:
3 + 3/11 = 36/11 or 3.27 hours

The distance when she meets her brother is:
D = RT
D = 5(36/11)
D = 180/11
D = 16.36, about 16.4 miles ---> choose answer (B)

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