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 Monday, if the difference between the time taken by the boat to go upstream and to go downstream is 20 hours, then what is the total time taken by the boat to go upstream and downstream?
The total time taken upstream and downstream on Monday is 60 hours.
The speed of stream is 4 km/h and the distance is 320 km each way.
Let the speed of boat be x, so downstream speed is x plus 4 and upstream speed is x minus 4.
The time difference gives 320 over x minus 4 minus 320 over x plus 4 equals 20.
Solving gives x squared equals 144, so x equals 12 km/h.
Downstream time is 320 over 16, that is 20, and upstream time is 320 over 8, that is 40.
The total time is 20 plus 40, which is 60 hours.
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