If a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day?
(A) 100
(B) 120
C) 140
(D) 150
(E) 160
70 miles are covered in the extra hour, implying a rate of 70 miles per hour.
This rate is 5 miles faster than the actual rate.
Thus, 10 miles faster than the actual rate = 70+5 = 75 miles per hour.
Distance traveled in 2 hours = r*t = 75*2 = 150 miles.
The correct answer is
D.
We also could plug in the answers, which represent the distance traveled in the extra 2 hours.
Answer choice C: 140 miles.
Rate = d/t = 140/2 = 70 miles per hour.
This rate is 10 miles per hour faster than the actual rate
Thus, 5 miles per hour faster than the actual rate = 70-5 = 65 miles per hour.
Distance traveled at this rate in 1 hour = 65 miles.
The problem states that 70 miles are covered in the extra 1 hour, so a bigger answer choice is needed.
Eliminate A, B and C.
Answer choice D: 150 miles.
Rate = d/t = 150/2 = 75 miles per hour.
This rate is 10 miles per hour faster than the actual rate
Thus, 5 miles per hour faster than the actual rate = 75-5 = 70 miles per hour.
Distance traveled at this rate in 1 hour = 70 miles.
Success!
The correct answer is
D.
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