AndreG wrote:
If it took a bus 4 hours to get from town A to town B, what was the average speed of the bus for the trip?
1. In the first 2 hours the bus covered 100 miles.
2. The average speed of the bus for the first half of the distance was twice its speed for the second half.
(C) 2008 GMAT Club - m16#8
I am always really struggling with these... I can easily determine (at least something...) that it has to be C,E - but I usually have to guess then! Any help greatly appreciated! THANKS
To know the average speed, we need total distance & total time. We know time=4h, so just need distance
(1) We only know 100miles covered in first 2 hours. Don't know about rest of the distance covered. Insufficient
(2) Avg speed was halfed in the second half. But we dont know what it actually was, so can't put a number to it. Insufficient
(1+2) Avg speed in first 2hours 50mph, distance is 100miles. Lets say distance covered in total is x.
For x/2 it went for speed s ... time taken = (x/2s)
For x/2 it went for speed s/2 ... time taken = (x/s)
(x/s) + (x/2s) = 4hrs ... (x/2s) = 4/3 hrs
Which means for 4/3 hours it went for speed s and then for the rest of the time the speed doubled.
So consider the first 2hours, (4/3)*s + (2/3)*(s/2) = 100 ... s=300/5=60
We know, we can know s/2 ... we can find out total distance covered = 60*(4/3) + 30*(8/3) = 160
So we can find out average speed = 160/4 = 40miles/hour
Sufficient
Answer is (C)Where did u get E from ?
speed for the second half.
Then for (1)+(2) we would have: \(s_1*\frac{4}{3}+\frac{s_1}{2}*(2-\frac{4}{3})=100\) --> we can find \(s_1\) so we can find \(d\) (\(d=2*s_1*\frac{4}{3}\)). But as it is we don't know whether the average speed after first \(\frac{4}{3}\) hours till 2 hours from the start was \(\frac{s_1}{2}\) or less or more, we just know that the average speed from first \(\frac{4}{3}\) hours till 4 hours from the start was \(\frac{s_1}{2}\).