The table shows, for a boat over five days (Monday to Friday), the distance travelled upstream (km), speed of boat (km/h), speed of stream (km/h) and total time (hours). Dashes are missing and to be calculated. Distance upstream = distance downstream; total time = downstream time + upstream time.
| Day | Distance Upstream (km) | Speed of Boat (km/h) | Speed of Stream (km/h) | Total Time (hours) |
|---|---|---|---|---|
| Monday | 320 | — | 4 | — |
| Tuesday | — | — | — | 75 |
| Wednesday | 270 | — | 6 | — |
| Thursday | — | 11 | 7 | — |
| Friday | 324 | — | — | 72 |
On Friday, if the ratio of speed of boat to speed of stream is 2:1, then what is the difference between the time taken by the boat to go upstream and to go downstream?
The difference between upstream and downstream time on Friday is 36 hours.
Let the speed of boat be 2x and speed of stream be x, so the ratio is 2:1.
Upstream speed is 2x minus x, which is x, and downstream speed is 2x plus x, which is 3x.
Total time is 324 over x plus 324 over 3x, which equals 72.
This gives 1296 over 3x equals 72, so x equals 6.
Upstream time is 324 over 6, that is 54, and downstream time is 324 over 18, that is 18.
The difference is 54 minus 18, which is 36 hours.
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