Judy averaged 42 miles per hour mph driving from Allentown t

Judy averaged 42 miles per hour (mph) driving from Allentown to Harrisburg and 51 mph driving from Harrisburg to Pittsburgh. See the accompanying figure. Ifshe drove a total of 288 miles in 6 hours, then how long did it take her to drive from Harrisburg to Pittsburgh?

Solution

A to H DATA:
rate = 42 mph ; distance = x miles ; time = x/42 hrs.
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H to P DATA:
rate = 51 mph ; distance = 288-x miles ; time = (288-x)/51 hrs
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EQuATION:
time + time = 6 hrs
x/42 + (288-x)/51 = 6
51x + 42*288 - 42x = 6*42*51
9x = 42(6*51-288)
x = 42*18/9
x = 84 miles
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H to P
distance: 288-x = 204
time = 204/51 = 4 hrs.