Two buses leave a station at the same time and travel in opposite directions. One bus travels 12 mi/hr faster than the other. If the two buses are 750 miles apart after 5 hours, what is the rate of each bus?
Accepted Solution
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Answer: speed of the first bus is 81 miles per hour.speed of the second bus is 69 miles per hour.Step-by-step explanation:Let x = the speed of the first busLet y = speed of the second busOne bus travels 12 miles/hour faster than the other. Assuming that the first bus travels at a faster rate, thenx = y + 12Recall that distance = speed Γ time.The distance travelled by the first bus in 5 hours would be x Γ 5 = 5xThe distance travelled by the second bus in 5 hours would be y Γ 5 = 5ythe two buses are 750 miles apart after 5 hours. This means that total distance travelled by first bus and second bus in 5 hours is equal to 750 miles. Therefore,5x + 5y = 750 - - - - - - - -- - 1Substituting x = y + 12 into equation 1, it becomes5(y+12) + 5y = 7505y + 60 + 5y = 7505y + 5y = 750 - 6010y = 690y = 690/10 = 69 miles per hourx = y + 12 = 69 + 12 x = 81 miles per hour