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 Wednesday, if the boat covered half of the distance upstream with its usual speed and the other half with double its speed, and it takes 33 and three-fourth hours less than the usual time to go upstream, then what is the total time taken by the boat to go upstream and downstream?
The total time taken upstream and downstream on Wednesday is 108 hours.
The distance is 270 km and the speed of stream is 6 km/h.
Let the usual boat speed be x, so usual upstream speed is x minus 6.
Splitting the trip into two halves and equating the time saved to 33 and three-fourth hours forms a quadratic.
Solving x squared minus 11x plus 18 equals 0 gives x equals 9 km/h.
Upstream time is 270 over 3, that is 90, and downstream time is 270 over 15, that is 18.
The total time is 90 plus 18, which is 108 hours.
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