Table shows the average speed (km/h) of five trains A to E from Monday to Saturday. Dashes are missing values to be calculated if required.
| Train | Mon | Tue | Wed | Thu | Fri | Sat |
|---|---|---|---|---|---|---|
| A | 72 | 80 | — | 64 | 54 | — |
| B | 88 | — | 80 | — | 72 | 90 |
| C | 54 | 70 | 72 | — | 64 | 60 |
| D | — | 120 | 95 | — | 90 | 110 |
| E | 72 | 80 | 84 | 75 | — | — |
Train D runs 150 km more on Monday than on Thursday, and the times taken by the train on Monday and Thursday are 5 hours and 4 hours respectively. If the average speed of this train on Monday is 15 km per hour more than that on Thursday, then the mean of the distances travelled by the train on Monday and Thursday is
The mean of the two distances is 375 km, so the answer is 375 km.
Let the Thursday distance be x and the Thursday speed be y.
The Thursday distance is speed times time, so x equals 4y.
The Monday distance is x plus 150 and equals the Monday speed y plus 15 times 5 hours.
So x plus 150 equals 5y plus 75, giving x equal to 5y minus 75.
Solving 4y equal to 5y minus 75 gives y equal to 75, so the Thursday distance is 300 and Monday is 450.
The mean of 300 and 450 is 750 divided by 2, which is 375 km.
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