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Difficulty:
45%
(medium)
Question Stats:
68% (02:31) correct
32%
(02:48)
wrong
based on 1136
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A cruise ship travels between two islands, Island A and Island B, which are 120 miles apart. The cruise ship operates at a constant speed in still water. However, a current flows at a constant speed of 3 miles per hour.
On the trip from Island A to Island B, the ship travels with the current and completes the journey in 4 hours. On the return trip, against the current, it takes longer to complete the journey.
Based on the above information, select for Still Speed the cruise ship’s speed in still water, in miles per hour and for Average Speed the ship’s average speed for the round trip, in miles per hour.
On the trip from Island A to Island B, the ship travels with the current and completes the journey in 4 hours. On the return trip, against the current, it takes longer to complete the journey.
Based on the above information, select for Still Speed the cruise ship’s speed in still water, in miles per hour and for Average Speed the ship’s average speed for the round trip, in miles per hour.
| Still Speed | Average Speed | |
| 24 | ||
| 25.4 | ||
| 26 | ||
| 26.7 | ||
| 27 | ||
| 28 |
1. We need to find the boat’s normal speed and its average speed for the round trip.
2. Let the boat’s normal speed be x. Traveling from Island A to B is with the current, which means the total speed is x + 3.
Then we can put together an equation: \(x + 3 = \frac{120}{4} = 30 \rightarrow x = 27\)mph.
3. Now to find the average speed, we also need to consider the trip from Island B to A.
The time it takes for this trip is \(\frac{120}{27 - 3} = 5\) hours.
4. The average speed equals the total distance traveled divided by the total time or \(\frac{120 + 120}{4 + 5} \approx 26.7\) mph.
5. Our answer will be: Still Speed - 27 mph; Average Speed - 26.7 mph.
BoatIslands1.jpg [ 18.91 KiB | Viewed 7049 times ]
BoatIslands2.jpg [ 18.95 KiB | Viewed 7028 times ]
2. Let the boat’s normal speed be x. Traveling from Island A to B is with the current, which means the total speed is x + 3.
Then we can put together an equation: \(x + 3 = \frac{120}{4} = 30 \rightarrow x = 27\)mph.
3. Now to find the average speed, we also need to consider the trip from Island B to A.
The time it takes for this trip is \(\frac{120}{27 - 3} = 5\) hours.
4. The average speed equals the total distance traveled divided by the total time or \(\frac{120 + 120}{4 + 5} \approx 26.7\) mph.
5. Our answer will be: Still Speed - 27 mph; Average Speed - 26.7 mph.
Attachment:
BoatIslands1.jpg [ 18.91 KiB | Viewed 7049 times ]
Attachment:
BoatIslands2.jpg [ 18.95 KiB | Viewed 7028 times ]
General Discussion
The speed of the Current Sc= 3 miles/hr
The speed of the boat be = Sb
From above table with A to B data,
We can find Sb=27 miles/hr
Sb+3 = 120/4
Sb=27 miles/hr
From B to A,
27-3=120/t
t = 5 hrs
Hence Average speed = 240/9 = 26.7 miles/hr
The speed of the boat be = Sb
| speed | Distance | Time | |
| A to B | Sb + 3 | 120 | 4 hrs |
| B to A | Sb-3 | 120 | t |
From above table with A to B data,
We can find Sb=27 miles/hr
Sb+3 = 120/4
Sb=27 miles/hr
From B to A,
27-3=120/t
t = 5 hrs
Hence Average speed = 240/9 = 26.7 miles/hr
when moving with current = Sb + 3mph = 120miles/4hrs
Sb = 27mph
Speed on forward journey = 27+3 = 30mph
Speed on return journey = 27-3 =24mph
Average Speed = 2ab/a+b = 2(30)(24)/30+24 = 26.7mph
Sb = 27mph
Speed on forward journey = 27+3 = 30mph
Speed on return journey = 27-3 =24mph
Average Speed = 2ab/a+b = 2(30)(24)/30+24 = 26.7mph
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