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24 Jun 2013, 14:15
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B
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Difficulty:
85%
(hard)
Question Stats:
57% (03:17) correct
43%
(03:17)
wrong
based on 176
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Two buses are travelling on the highway from X to Y . The speed of the first bus is 60KMPH and the second bus travels at the speed of 40KMPH. The first bus leaves at 11 AM and the second leaves 15 mins later. The first bus starts back for X, 15 mins after it reaches Y . How far from Y will the first Bus meet the second ?Also, after how much time will they meet each other after the departure of the first bus from X , if the distance between X and Y is 180 KM.
A)36 KM , 3 Hrs 36 Mins
B)36 KM, 3 Hrs 51 Mins
c)24KM, 3 Hrs 50 mins
d)24 KM, 3 hrs 51 mins
e)48 KM, 2 Hrs 51 mins
A)36 KM , 3 Hrs 36 Mins
B)36 KM, 3 Hrs 51 Mins
c)24KM, 3 Hrs 50 mins
d)24 KM, 3 hrs 51 mins
e)48 KM, 2 Hrs 51 mins
24 Jun 2013, 16:50
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This problem is best to do in steps, since you have to find out how far the buses go and then come back... you could do the math into one, giant equation but it's easier to segment it out and draw a timeline, especially since we don't have a calculator. .
So it takes the first bus \(\frac{180km}{60mph} = 3:00 hours\) to get to point Y. It then waits there another 15 minutes...
The second bus waits 15 minutes and then starts heading for y at \(40mph\)
this means that at the time the first bus leaves point Y, the second bus will have been travelling for 3:00 hours \((3:15-15)\)
Which means that it will have covered \(40mph * 3:00 hours = 120m\)
Which means that they are now 3:15 into the journey and \(180m - 120m =60m\) apart...
The two of them, together, can close the distance in \(\frac{60m}{(40mph + 60mph)} = .6 hours = 36 minutes\)
So the total time before they meet is \(3:15 + 36= 3:51minutes\)
The total distance away from point X of the second bus would be \(120m + (40mph * .6hours) = 144 miles\) which means that the bus has \(180-144= 36 miles\) left to go.
So the final answer is B.
So it takes the first bus \(\frac{180km}{60mph} = 3:00 hours\) to get to point Y. It then waits there another 15 minutes...
The second bus waits 15 minutes and then starts heading for y at \(40mph\)
this means that at the time the first bus leaves point Y, the second bus will have been travelling for 3:00 hours \((3:15-15)\)
Which means that it will have covered \(40mph * 3:00 hours = 120m\)
Which means that they are now 3:15 into the journey and \(180m - 120m =60m\) apart...
The two of them, together, can close the distance in \(\frac{60m}{(40mph + 60mph)} = .6 hours = 36 minutes\)
So the total time before they meet is \(3:15 + 36= 3:51minutes\)
The total distance away from point X of the second bus would be \(120m + (40mph * .6hours) = 144 miles\) which means that the bus has \(180-144= 36 miles\) left to go.
So the final answer is B.
Time for 1st bus travels from X to Y = 180/60 = 3h
Time for 2nd bus travels from X to Y = 180/30 = 4.5h
Because 1st bus traveled faster ==> 1st bus must meet 2nd when 1st bus went back from Y to X
t = time 2nd bus traveled to meet 1st bus
==> 2nd bus's distant = 40t
==> 1st bus's distant = 180 + 60(t - 3 + 1/4 - 1/4) because 1st bus started 15m (1/4h) earlier than 2nd bus, but waited 15m (1/4h) before traveling back to X.
We have equation: 40t + 60(t - 3) = 180
==> t = 3.6 h = 3h and 36 minutes
Question #1: How far from Y will the first Bus meet the second?
distant from Y = 60(3.6 -3) = 36km
Question #2: how much time will they meet each other after the departure of the first bus from X?
Time = time 2nd bus traveled to meed 1st bus + 15 minutes = 3h 36minutes + 15minutes = 3h 51 minutes.
Hence, B is correct.
Hope it helps.
Time for 2nd bus travels from X to Y = 180/30 = 4.5h
Because 1st bus traveled faster ==> 1st bus must meet 2nd when 1st bus went back from Y to X
t = time 2nd bus traveled to meet 1st bus
==> 2nd bus's distant = 40t
==> 1st bus's distant = 180 + 60(t - 3 + 1/4 - 1/4) because 1st bus started 15m (1/4h) earlier than 2nd bus, but waited 15m (1/4h) before traveling back to X.
We have equation: 40t + 60(t - 3) = 180
==> t = 3.6 h = 3h and 36 minutes
Question #1: How far from Y will the first Bus meet the second?
distant from Y = 60(3.6 -3) = 36km
Question #2: how much time will they meet each other after the departure of the first bus from X?
Time = time 2nd bus traveled to meed 1st bus + 15 minutes = 3h 36minutes + 15minutes = 3h 51 minutes.
Hence, B is correct.
Hope it helps.
