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7/12X-1/4X

when fritz drives to work his trip is 35 minutes, but when he takes the train it takes 15 minutes. find the distance fritz travels to work if the train travels 80 miles per hour faster than his driving.

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Rajesh P. | Effective Tutor for Test Prep, Math, Science, Comp Science, BusinessEffective Tutor for Test Prep, Math, Sci...
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Let driving speed of Fritz = X miles per hour
so train speed = X+80 miles per hour
Train travels for 15 minutes = 15/60 = 1/4 hours
Distance travelled by train = speed x time = (X+80) x 1/4 = (X+80)/4 = (X/4 +20) miles
Fritz travels for 35 minutes = 35/60 = 7/12 hours
Distance travelled by fritz in 35 minutes = speed x time = X x 7/12 = 7X/12 miles

Now distance travelled by train = distance driven by Fritz
X/4 + 20 = 7X/12
X/4 + 20 - X/4 = 7X/12 - X/4
20 = 7X/12 - (X/4)x(3/3) = 7X/12-3X/12
20 = (7-3)X/12 = 4X/12 = X/3
20 x 3 = (X/3) x 3
X = 60 miles/jour
Distance travelled by Fritz to work = 7X/12=7x60/12 = 35 miles

Let us check the answer
Distance travelled by train = speed of train x time taken by train = (60+80) x 1/4 = 140/4 = 35 miles
so distance travelled by train = distance driven by Fritz (Answer is verified)