Same pattern as Bus and car — the catch-up. New numbers, new
story. Try each one on paper, then check the working below — or watch it drawn out, the
same way the problem above is.
Question 1
Town A and Town B are 315 km apart along one road. A car leaves Town A at 60 km/h and a lorry leaves Town B at 45 km/h. They set off at the same time, towards each other. How far from Town A do they meet?
A bus is 15 km ahead of a car on the same expressway. The bus travels at 75 km/h and the car at 80 km/h. Both keep to those speeds, and the car sets off after the bus. How far has the bus gone when the car catches it?
A bus is 125 km ahead of a car on the same expressway. The bus travels at 45 km/h and the car at 70 km/h. Both keep to those speeds, and the car sets off after the bus. How far has the bus gone when the car catches it?
A bus is 150 km ahead of a car on the same expressway. The bus travels at 40 km/h and the car at 70 km/h. Both keep to those speeds, and the car sets off after the bus. How long does the car take to catch up with the bus?
A bus is 60 km ahead of a car on the same expressway. The bus travels at 30 km/h and the car at 40 km/h. Both keep to those speeds, and the car sets off after the bus. How far has the bus gone when the car catches it?
They are travelling towards each other, so in one hour they close 60 km and 45 km — 105 km of the gap between them.60 + 45 = 105 km/h
The gap is 315 km, and it closes at that rate every hour.315 ÷ 105 = 3 hours
Both of them travelled for those same 3 hours — that is the fact the rest hangs on.The car: 60 × 3 = 180 km
And so did the other.The lorry: 45 × 3 = 135 km
Because the time was the same, the two distances are in the ratio of the two speeds.180 : 135 = 60 : 45
They meet 180 km from Town A.
The pattern. Each hour they close 60 + 45 = 105 km of the gap between them. They travel for the same length of time, so their distances end up in the ratio 60 : 45.
The car is 15 km behind and travelling faster, so what matters is how fast the gap between them shrinks.80 − 75 = 5 km/h
The gap is 15 km, and it closes at that rate every hour.15 ÷ 5 = 3 hours
Both of them travelled for those same 3 hours — that is the fact the rest hangs on.The bus: 75 × 3 = 225 km
And so did the other.The car: 80 × 3 = 240 km
Because the time was the same, the two distances are in the ratio of the two speeds.225 : 240 = 75 : 80
The bus has gone 225 km.
The pattern. Only the difference between the speeds closes the gap: 80 − 75 = 5 km/h. They travel for the same length of time, so their distances end up in the ratio 75 : 80.
The car is 125 km behind and travelling faster, so what matters is how fast the gap between them shrinks.70 − 45 = 25 km/h
The gap is 125 km, and it closes at that rate every hour.125 ÷ 25 = 5 hours
Both of them travelled for those same 5 hours — that is the fact the rest hangs on.The bus: 45 × 5 = 225 km
And so did the other.The car: 70 × 5 = 350 km
Because the time was the same, the two distances are in the ratio of the two speeds.225 : 350 = 45 : 70
The bus has gone 225 km.
The pattern. Only the difference between the speeds closes the gap: 70 − 45 = 25 km/h. They travel for the same length of time, so their distances end up in the ratio 45 : 70.
The car is 150 km behind and travelling faster, so what matters is how fast the gap between them shrinks.70 − 40 = 30 km/h
The gap is 150 km, and it closes at that rate every hour.150 ÷ 30 = 5 hours
Both of them travelled for those same 5 hours — that is the fact the rest hangs on.The bus: 40 × 5 = 200 km
And so did the other.The car: 70 × 5 = 350 km
Because the time was the same, the two distances are in the ratio of the two speeds.200 : 350 = 40 : 70
The car catches up after 5 hours.
The pattern. Only the difference between the speeds closes the gap: 70 − 40 = 30 km/h. They travel for the same length of time, so their distances end up in the ratio 40 : 70.
The car is 60 km behind and travelling faster, so what matters is how fast the gap between them shrinks.40 − 30 = 10 km/h
The gap is 60 km, and it closes at that rate every hour.60 ÷ 10 = 6 hours
Both of them travelled for those same 6 hours — that is the fact the rest hangs on.The bus: 30 × 6 = 180 km
And so did the other.The car: 40 × 6 = 240 km
Because the time was the same, the two distances are in the ratio of the two speeds.180 : 240 = 30 : 40
The bus has gone 180 km.
The pattern. Only the difference between the speeds closes the gap: 40 − 30 = 10 km/h. They travel for the same length of time, so their distances end up in the ratio 30 : 40.