SOLUTION: Two buses leave towns 484 kilometers apart at the same time and travel toward each other. One bus travels 18 km/h faster than the other. If they meet in 2 hours, what is the rate o

Question 1192495: Two buses leave towns 484 kilometers apart at the same time and travel toward each other. One bus travels 18 km/h faster than the other. If they meet in 2 hours, what is the rate of each bus.
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39614)   (Show Source): You can put this solution on YOUR website!
Fast bus, r+18
Slow bus, r
2 hours

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Answer by ikleyn(52756)   (Show Source): You can put this solution on YOUR website!
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Two buses leave towns 484 kilometers apart at the same time and travel toward each other.
One bus travels 18 km/h faster than the other. If they meet in 2 hours, what is the rate of each bus.
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Let x be the average rate of the slower bus, in kilometers per hour. Then the rate of the other base is (x+18) km/h. One bus' traveled distance is 2x kilometers. The other bus' traveled distance is 2*(x+18) kilometers. The total distance equation is 2x + 2*(x+18) = 484 kilometers. Simplify and find x 2x + 2x + 36 = 484 4x = 484 - 36 4x = 448 x = 448/4 = 112. ANSWER. The slower bus rate is 112 km/h. The faster bus rate is 112+18 = 130 km/h. CHECK. 112*2 + 130*2 = 484 kilometers, the total distance. ! Precisely correct !

Solved.

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Answer by greenestamps(13196)   (Show Source): You can put this solution on YOUR website!

A somewhat informal solution, using a problem-solving "trick"....

They meet in 2 hours after being 484km apart; their combined speed is 484/2 = 242 km/h.

If they were traveling at the same speed, the rate of each would be 242/2=121 km/h.

For the difference in their speeds to be 18 km/h, one of them must have been traveling 9 km/h faster than 121 km/h and the other must have been traveling 9 km/h slower than 121 km/h.

ANSWERS: The speeds of the two buses were 121+9 = 130 km/h and 121-9 = 112 km/h.

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