A ship travels downstream at a speed of 77 km/h and upstream at a speed of 67 km/h. It takes 15 seconds to cross a pole in still water at the same speed. Another small boat in still water takes 80 seconds to cross a dockyard at a speed of 36 km/h.
Given this information, answer the following:
- What are the speeds of the ship in still water and the stream?
- How long will it take for the ship to cross the dockyard in still water?
- What are the lengths of the ship and the dockyard?
Speeds of the Ship in Still Water and the Stream
Let vs be the speed of the ship in still water and vc be the speed of the current.
The downstream speed vd is given by: vd=vs+vc=77 km/h
The upstream speed vu is given by: vu=vs−vc=67 km/h
Adding and subtracting these two equations: vs+vc+vs−vc=77+67 2vs=144 vs=72 km/h
vs+vc−(vs−vc)=77−67 2vc=10 vc=5 km/h
Therefore, the speed of the ship in still water is 72 km/h and the speed of the stream is 5 km/h
Ship’s Speed:
Imagine the water current is like a moving sidewalk helping the ship downstream and slowing it upstream. Here’s how to find the ship’s speed and the current’s speed:
Ship Crossing the Dockyard:
To find how long the ship takes to cross the dockyard in still water, we can use a simple trick:
Lengths (Optional):
Unfortunately, with the given information, we cannot determine the exact lengths of the ship and the dockyard. We only know the speeds and times.
Ship’s Speed:
Imagine the water current is like a moving sidewalk helping the ship downstream and slowing it upstream. Here’s how to find the ship’s speed and the current’s speed:
Ship Crossing the Dockyard:
To find how long the ship takes to cross the dockyard in still water, we can use a simple trick:
Lengths (Optional):
Unfortunately, with the given information, we cannot determine the exact lengths of the ship and the dockyard. We only know the speeds and times.