Video: US-SAT02S4-Q31-415198410359

A race car reaches 870 metres in 18.6 seconds. If the car travels at the same rate, which of the following is closest to the distance that the car will reach in 2 min? [A] 1,750 metres [B] 8,100 metres [C] 2,250 metres [D] 5,600 metres

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Video Transcript

A race car reaches 870 metres in 18.6 seconds. If the car travels at the same rate, which of the following is closest to the distance that the car will reach in two minutes? Is it A) 1750 metres, B) 8100 metres, C) 2250 metres, or D) 5600 metres?

There are lots of ways of approaching this problem. We will look at two different methods. Firstly, we need to ensure that our measurements are in the same units. One minute is equal to 60 seconds. This means that two minutes is equal to 120 seconds, as 60 multiplied by two equals 120. We want to calculate the distance that the car would reach in 120 seconds.

We’re told in the question that the car reaches 870 metres in 18.6 seconds. We could therefore work out the distance it reaches in one second by dividing by 18.6. 870 divided by 18.6 is equal to 46.77419 and so on. Therefore, in one second, the car reaches 46.77419 metres.

We can now calculate how far the car would travel in 120 seconds by multiplying by 120. Multiplying 46.77419 by 120 gives us 5612.903. As the number after the decimal point, the nine, is greater than five, we can round up to the nearest metre. In two minutes, the car would reach a distance of 5613 metres to the nearest metre. As the distance travelled was 5613, we can see that the correct answer was option D 5600 metres. This is the answer that is closest to the distance the car will reach in two minutes.

An alternative method would be to use our speed-distance-time triangle. This reminds us of the formula that speed is equal to distance divided by time. The distance can be calculated by multiplying speed by time. And finally, time can be calculated by dividing distance by speed.

We were told initially that the car reached a distance of 870 metres in a time of 18.6 seconds. This means that we could calculate the speed by dividing 870 by 18.6, as speed is equal to distance divided by time. 870 divided by 18.6 is equal to 46.77 and so on. This means that the speed travelled to two decimal places is 46.77 metres per second.

We were asked to calculate the distance travelled in 120 seconds. The speed was constant as the car travels at the same rate. Therefore, the speed is equal to 46.77 and the time is equal to 120 seconds. As the distance is equal to the speed multiplied by the time, we can multiply 46.77 by 120, which gives us an answer of 5613 metres to the nearest metre. Once again, we can see that the closest distance of the four options is option D 5600 metres.

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