A large ship moving at 14 mph in the river has an investigator cater swimming beside it. Investigator cater sets out to survey 70 miles downstream in the direction that the ship is headed. If the cater's speed is 28 mph, how much time will the cater spend surveying and coming back to the ship?
A. 2 hours 30 minutes
B. 2 hours 45 minutes
C. 3 hours 15 minutes
D. 3 hours 20 minutes
E. 3 hours 40 minutes
D
A large ship moving at 14 mph in the river has an investigator cater swimming beside it
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My guess is D 3 hour 20 min
In 2 hour 30 min ship will travel 35 miles and cater will complete survey of 70 miles.
In additional 50 min ship will complete ~ 11.5 miles down stream and cater will upstream ~23 miles with assumption upstream speed is equivalent to down stream speed.
In 2 hour 30 min ship will travel 35 miles and cater will complete survey of 70 miles.
In additional 50 min ship will complete ~ 11.5 miles down stream and cater will upstream ~23 miles with assumption upstream speed is equivalent to down stream speed.
Since, the investigation cater is surveying downstream 70 miles and the speed of investigation cater is 28 mph,
Time taken to reach the spot = 70/28 = 2 hours 30 minutes.
Now in this time, the ship will also travel some distance.
The Distance travelled by the ship = 14 *2.5 miles = 35 miles.
Now, the ship is 35 miles far from investigation carter, and since they are travelling towards each other,
Time to meet = 35/(28 + 14) = 50 minutes.
Thus, total time = 3 hours 20 minutes.
Time taken to reach the spot = 70/28 = 2 hours 30 minutes.
Now in this time, the ship will also travel some distance.
The Distance travelled by the ship = 14 *2.5 miles = 35 miles.
Now, the ship is 35 miles far from investigation carter, and since they are travelling towards each other,
Time to meet = 35/(28 + 14) = 50 minutes.
Thus, total time = 3 hours 20 minutes.