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But the explanation at the end of the test doesn't seem to take into account the fact that Bill stopped along the way and that time has to be excluded.

Guys this one is has sent me into an infinite loop :p

13. If he did not stop along the way, what speed did Bill average on his 3-hour trip? (1) He travelled a total of 120 miles. (2) He travelled half the distance at 30 miles per hour and half the distance at 60 miles per hour.

The answer is D (each statement alone is sufficient). But the explanation at the end of the test doesn't seem to take into account the fact that Bill stopped along the way and that time has to be excluded.

If he did not stop along the way, what speed did Bill average on his 3-hour trip?

The stem explicitly states that Bill did not stop along the way, so your doubt is not valid.

(1) He travelled a total of 120 miles --> (average speed) = (total distance traveled) / (time spent) --> (average speed) = 120/3 = 40 miles per hour. Sufficient.

(2) He travelled half the distance at 30 miles per hour and half the distance at 60 miles per hour --> (d/2)/30+(d/2)/60=3 (the time spent for the first half of the distance would be (distance traveled) / (speed)=(d/2)/30 and the time spent for the second half of the distance would be (distance traveled) / (speed)=(d/2)/60)). Solving (d/2)/30+(d/2)/60=3 for d: d=120 miles --> (average speed) = 120/3 = 40 miles per hour. Sufficient.

Or: as he traveled d/2 mile at 30 miles per hour and then the same distance of d/2 at 30*3=60 miles per hour (twice the previous speed) then he must have spent twice as much time for the first half as for the second (t1/t2=2/1), so as he spent total of 3 hours on the entire trip then he must have spent 2 hours for the first half and 1 hour for the second: d=2*30+1*60=120 --> (average speed) = 120/3 = 40 miles per hour. Sufficient.

Re: If he did not stop along the way, what speed did Bill averag [#permalink]

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29 Jul 2013, 15:35

If he did not stop along the way, what speed did Bill average on his 3-hour trip?

(1) He travelled a total of 120 miles. We are given time it took him to travel 120 miles. Let's say we break this trip into two 60 mile segments. If he went at 40 miles/hour for the first half he would have to travel a certain speed for the second portion to cover the 60 miles in time. Regardless of what speed he travels over any given portion of the trip he must travel at the same average speed to cover 120 miles in 3 hours. SUFFICIENT

(2) He travelled half the distance at 30 miles per hour and half the distance at 60 miles per hour.

Solely based on intuition, I think this is enough to solve. If he went half the distance at 30 miles per hour he could have traveled two hours and covered 60 miles. He then could have traveled one hour at 60 miles per hour, covered 60 miles and traveled a total of 120 miles over three hours. SUFFICIENT

(D)

P.S. could someone explain the algebra to me for #2? I am still a bit confused as to why we solve for time when we are looking for speed.

(1) Sufficient. With the distance known, we could plug it into the rate formula and computer Bill's rate.

(2) Sufficient. If he covered the same distance at 30 mph as he did at 60 mph, he must have been travelling at 30 mph for twice as long as he was at 60 mph. Given that he travelled for 3 hours, he travelled at 30 mph for 2 hours and 60 mph for 1 hour. That comes to 120 miles total distance, and again we solve for the rate. _________________

Re: If he did not stop along the way, what speed did Bill averag [#permalink]

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