B i left boston for washington, dc, at 7:00 am. at first, my speed was 55 mph; then it was 75 mph. i traveled 630 miles in 10 hours. at what time did i begin to drive faster?
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B i left Boston for Washington, dc, at 7:00 am.
The speed in the beginning = 55 mph
The speed at the end = 75 mph
Distance from Boston to Washington D.C. = 630 miles (given)
Time of the travel = 10 hours
Let "x" be the distance we drove at 55 mph and 630 - x the distance we drove at 75 mph, thus we have,
Time of the travel = Time we drove at 55 mph + Time we drove at 75 mph
10 = x/55 + (630 - x)/75
41250 = 75x + 55 × (630 - x) (LCM = 4,125)
41250 = 75x + 34,650 - 55x
20x = 41,250 - 34,650
20x = 6,600
x = 6,600/20
∴ x = 330
⇒ 630 - x = 300
Time we drove with 55 mph = 330/55 = 6 hours
Time we drove with 75 mph = 300/75 = 4 hours
We began to drive faster at 1:00 p.m. (7 am + 6 hours)
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