The following table shows the distance travelled by a boat moving upstream (in…
2023
The following table shows the distance travelled by a boat moving upstream (in km) during five different days of a week from Monday to Friday, along with the speed of boat (in km/hour), speed of stream (in km/hour) and total time taken (in hours). Some data is missing in the table (indicated as '—') that you are expected to calculate, if required. Based on the data in the table, answer the questions that follow.
Day-wise distance travelled by the boat and other details
Days | Distance Upstream (km) | Speed of Boat (km/hour) | Speed of Stream (km/hour) | Total Time Taken (hours) |
|---|---|---|---|---|
Monday | 320 | — | 4 | — |
Tuesday | — | — | — | 75 |
Wednesday | 270 | — | 6 | — |
Thursday | — | 11 | 7 | — |
Friday | 324 | — | — | 72 |
Note: (1) Distance Upstream = Distance Downstream, if not stated otherwise.
Note: (2) Total Time Taken = Downstream Time + Upstream Time
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?
Answer: D. 60 hours — Concept: For a boat with still-water speed b and stream speed s, upstream speed is b - s and downstream speed is b + s. For equal distances d, time equals…
- A.
40 hours
- B.
30 hours
- C.
80 hours
- D.
60 hours
Show answer & explanation
Correct answer: D
Concept: For a boat with still-water speed b and stream speed s, upstream speed is b - s and downstream speed is b + s.
For equal distances d, time equals distance divided by speed; therefore the time difference can be used to determine b before adding the two travel times.
Application: Here d = 320 km, s = 4 km/h, and the upstream time exceeds the downstream time by 20 hours.
Let b km/h be the speed of the boat in still water. Then the upstream and downstream speeds are b - 4 and b + 4 km/h.
Write the given time difference: 320/(b - 4) - 320/(b + 4) = 20.
Combine the fractions: 320[(b + 4) - (b - 4)]/[(b - 4)(b + 4)] = 20, so 2560/(b2 - 16) = 20.
Hence b2 - 16 = 128, so b2 = 144. Since speed is positive and b > 4, b = 12 km/h.
The upstream time is 320/(12 - 4) = 40 hours, and the downstream time is 320/(12 + 4) = 20 hours.
Cross-check: 40 - 20 = 20 hours, which matches the given difference, and both legs cover 320 km at speeds 8 km/h and 16 km/h respectively.
Result: The total time is 40 + 20 = 60 hours.