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?
You've posted many math questions in the last couple of days. Most have been answered.
Now it's your turn. Please tell us what you don't understand about this problem. Then we'll be glad to help you.
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)
Well, I guess you could say the boy realized he was just going in circles and decided to turn back. Classic case of bike-cycle analysis! Ahem, anyways, let's crunch some numbers.
Since the boy is traveling at 6 miles per hour and his sister is traveling at 5 miles per hour, the boy has a speed advantage of 1 mile per hour. After 3 hours, the boy would have traveled 3 * 6 = 18 miles.
Now, let's look at the sister. During those 3 hours, she would have traveled 3 * 5 = 15 miles.
When the boy turns back, the distance between them is 18 - 15 = 3 miles. So, when they meet, the sister would have traveled 3 miles from the starting point.
I hope their biking adventure didn't tire them out too much, or they'll need a wheel-y long nap!
To solve this problem, we can follow these steps:
Step 1: Calculate the distance the boy has traveled after 3 hours.
Distance = speed × time
Distance = 6 miles/hour × 3 hours
Distance = 18 miles
Step 2: Determine the relative speed between the boy and his sister.
Relative Speed = Boy's Speed - Sister's Speed
Relative Speed = 6 miles/hour - 5 miles/hour
Relative Speed = 1 mile/hour
Step 3: Find the time it takes for the sister to travel the same distance as the boy.
Time = Distance / Relative Speed
Time = 18 miles / 1 mile/hour
Time = 18 hours
So, after 3 hours, the boy has traveled 18 miles, and the sister will have traveled 18 miles when they meet.
To solve this problem, we can break it down into smaller steps and use the equation:
Distance = Speed × Time.
1. Determine the distance the boy has traveled after 3 hours:
Distance Boy = Speed Boy × Time
= 6 miles/hour × 3 hours
= 18 miles
2. Since the boy turns back after 3 hours, he traveled back the same distance, so the distance between them decreases:
Distance Sister = Distance Boy - Distance Back
= 18 miles - Distance Back
3. The time taken by the sister is the same as the boy's time, i.e., 3 hours.
4. Using the equation for time, we can solve for the distance the sister has traveled:
Distance Sister = Speed Sister × Time
= 5 miles/hour × 3 hours
= 15 miles
Therefore, when they meet, the sister has traveled 15 miles from the starting point.