At 9am, Peter set off from Town A to Town B. At the same time, Tom drove along the same road from Town B to Town A. Peter travelled at a speed of 84km/h and Tom travelled at a speed of 78km/h throughout the whole journey. They met 30km from the middle of the journey. What is the distance between Town A and Town B?

is the ans 840km?

i think the anser is 810km.... idk

The answer key says 1620km, my answer is 810km ( x2 to get 1620), shouldn't be 840.

-Duplicated post-

Hi Jian Rong,

My working is as follows:

Let the distance be xkm
Peter speed is 84km/h
x/162 x 84 =84x/162(time taken by Peter)
Distance covered by Peter is 1/2x+30
Therefor
84x/162=1/2x+30
84x=81x+4860 (i.e. 84xx1=162x1/2x+162x30)
3x=4860
x=1620km
Distance between the two towns is 1620km

At 9am, Peter set off from Town A to Town B. At the same time, Tom drove along the same road from Town B to Town A. Peter travelled at a speed of 84km/h and Tom travelled at a speed of 78km/h throughout the whole journey. They met 30km from the middle of the journey. What is the distance between Town A and Town B?

For this speed question, we use the Common Time approach for speed where the Ratio of their distance is the same as the ratio of their speed.

Chris Rogers wrote:
At 9am, Peter set off from Town A to Town B. At the same time, Tom drove along the same road from Town B to Town A. Peter travelled at a speed of 84km/h and Tom travelled at a speed of 78km/h throughout the whole journey. They met 30km from the middle of the journey. What is the distance between Town A and Town B?

For this speed question, we use the Common Time approach for speed where the Ratio of their distance is the same as the ratio of their speed.



Although 1620km works when I try to check the answer, I'm still having difficulties trying to get the answer.

Peter --> 84km/h
Tom --> 78km/h

84-78=6
30/6=5
84+78=162
162x5=810

What is wrong with my working?

The problem is that you are dividing 30/6. You are doing this because you are taking the difference in distance divided by the difference in speed. However, the difference in distance is 60km not 30km. Why 60km? Because Peter is 30km beyond the midpoint and Tom is 30km less than the midpoint. So the difference traveled is 30km extra by Peter and 30km less by Tom --> 30km + 30km = 60km. When you divide 60km/6 you will arrive at the same answer.