Book Maths Puzzle Numerical Ability

Three cars travelling along a road in the same direction are, at a certain moment, in the following positions in relation to one another. Andrews is a certain distance behind Brooks, and Carter is twice that distance in front of Brooks. Each car travels at its own uniform rate of speed, with the result that Andrews passes Brooks in seven minutes, and passes Carter five minutes later. In how many minutes after Andrews would Brooks pass Carter?
86

Read Solution (Total 1)

Andrew speed : V1
Brooks speed: V2
Carter speed V3
In the initial position the distance (Andrew-Brooks) = d, the distance (Brooks- Carter) = 2d,

V1 = (d+x)/7 = d/7 + x/7
V2 = x/7
Means : V1 = V2+d/7 .......(1)

V1 = (3d+y)/12 = d/4 + y/12
V3 = y/12
Means: V1=V3+d/4 ..... (2)

From (1) & (2)
V2=V3 + 3d/28 ..... (3)

V2 = (2d+z)/t = 2d/t + z/t
V3=z/t
V2=V3 + 2d/t ....(4)

From (3) & (4):
t = 18 2/3
and T = 18 2/3 - 12 = 6 2/3

The answer is: 6 min 40 sec

Source:
https://www.weeklypuzzle.net/2020/09/the-03-cars-puzzle.html
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Book Other Question

Find the number of ways in which 5 men and 4 women can be seated round a table so that no two women are together solution A road is 300 miles long. A car, A, starts at noon from one end and goes throughout at 50 miles an hour, and at the same time another car, B, going uniformly at 100 miles an hour, starts from the other end together with a fly travelling 150 miles an hour. When the fly meets car A, it immediately turns and flies towards B. (1) When does the fly meet B? The fly then turns towards A and continues flying backwards and forwards between A and B. (2) When will the fly be crushed between the two cars if they collide and it does not get out of the way?