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 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?
Answer: A. 36 hours — CONCEPTFor a boat in a stream, downstream speed equals the boat’s still-water speed plus the stream speed, while upstream speed equals the boat’s still-water…
- A.
36 hours
- B.
42 hours
- C.
45 hours
- D.
35 hours
Attempted by 5 students.
Show answer & explanation
Correct answer: A
CONCEPT
For a boat in a stream, downstream speed equals the boat’s still-water speed plus the stream speed, while upstream speed equals the boat’s still-water speed minus the stream speed.
For equal distances, time equals distance divided by speed. Therefore, the total travel time is the sum of the upstream and downstream times.
APPLICATION
Let the stream speed be x km/h. Since the ratio of boat speed to stream speed is 2 : 1, the boat’s still-water speed is 2x km/h.
Upstream speed = 2x − x = x km/h, and downstream speed = 2x + x = 3x km/h.
The boat covers 324 km in each direction, so upstream time = 324/x hours and downstream time = 324/(3x) hours.
Using the total time, 324/x + 324/(3x) = 72.
Combining the fractions gives 432/x = 72, so x = 6 km/h.
Hence upstream time = 324/6 = 54 hours and downstream time = 324/18 = 18 hours.
CROSS-CHECK
The two times add to 54 + 18 = 72 hours, matching the table. Their inverse speed ratio is 18 : 6 = 3 : 1, which matches downstream speed 3x and upstream speed x.
Therefore, the time difference is 54 − 18 = 36 hours.