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 Tuesday, if the difference between the time taken by the boat to go upstream and downstream is 45 hours and the downstream speed is 24 km/hour, then what is the total distance covered by the boat to go upstream and downstream?
Answer: B. 720 km — CONCEPTFor equal upstream and downstream distances, write separate time equations for the two legs. When the total time and the difference of the times are…
- A.
680 km
- B.
720 km
- C.
740 km
- D.
540 km
Show answer & explanation
Correct answer: B
CONCEPT
For equal upstream and downstream distances, write separate time equations for the two legs. When the total time and the difference of the times are known, the two leg times are obtained by solving their sum and difference.
For any leg, distance equals speed multiplied by time. The round-trip distance is twice one leg distance when the two distances are equal.
APPLICATION
Let the upstream time be u hours and the downstream time be d hours.
The table gives u + d = 75, and the question gives u − d = 45.
Adding the equations gives 2u = 120, so u = 60 hours. Then d = 75 − 60 = 15 hours.
At the downstream speed of 24 km/hour, one-way distance = 24 × 15 = 360 km.
The upstream and downstream distances are equal, so total distance = 2 × 360 = 720 km.
CROSS-CHECK
Using 360 km for each leg gives downstream time 360 ÷ 24 = 15 hours and upstream time 60 hours. Their sum is 75 hours and their difference is 45 hours, so both conditions are satisfied. Therefore, the total distance is 720 km.