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7/12X-1/4X

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1 Answer

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)