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Maxwell leaves his home and walks toward Brad's house at the

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Maxwell leaves his home and walks toward Brad's house at the

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Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?

(A) 16
(B) 18
(C) 20
(D) 24
(E) 30

Is there a strategic approach to this question? Can any experts help?

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ardz24 wrote:
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?

(A) 16
(B) 18
(C) 20
(D) 24
(E) 30
Since Max and Brad travel toward each other, they WORK TOGETHER to cover the 50 kilometers between them.
When people work together, ADD THEIR RATES.
The combined rate for Max and Brad = 4+6 = 10 kilometers per hour.
Of every 10 kilometers traveled by Max and Brad working together, 4 kilometers are traveled by Max (since his rate is 4 kph), and 6 kilometers are traveled by Brad (since his rate is 6 kph).
Implication:
Brad will travel 6/10 of the 50 kilometers between the two houses:
(6/10)(50) = 30 kilometers.

The correct answer is E.

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ardz24 wrote:
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?

(A) 16
(B) 18
(C) 20
(D) 24
(E) 30

Is there a strategic approach to this question? Can any experts help?
If they were walking at the same speed for the same amount of time, they'd each cover half the distance, or 25 km. Because Brad is walking faster, he must cover more than 25 km. Only E works.

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BTGmoderatorAT wrote:
Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 50 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad?

(A) 16
(B) 18
(C) 20
(D) 24
(E) 30
We can let Maxwell’s time = t = Brad’s time. Furthermore, since distance = rate x time, Maxwell’s distance = 4t and Brad’s distance = 6t . Since their total distance is 50 km, we can create the following equation:

Maxwell’s distance + Brad’s distance = 50

4t + 6t = 50

10t = 50

t = 5

Thus, Brad has traveled 6(5) = 30 km when they meet.

Alternate Solution:

Since Brad and Maxwell are moving towards each other, the distance between the two is decreasing at a rate of 4 + 6 = 10 km/h. Since they are 50 km apart initially, they will meet after 50/10 = 5 hours. Thus, when they meet, Brad will have traveled 5 x 6 = 30 kilometers.

Answer: E

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