SOLUTION: A man traveled a distance of 960 kilometers by ship to an island. He returned by plane. The rate of the plane was 20 times the rate of the ship. He spent 42 hours on the trip. Find

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Question 1194355: A man traveled a distance of 960 kilometers by ship to an island. He returned by plane. The rate of the plane was 20 times the rate of the ship. He spent 42 hours on the trip. Find the rate of the ship and the rate if the plane.
Found 4 solutions by ankor@dixie-net.com, Alan3354, josgarithmetic, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
A man traveled a distance of 960 kilometers by ship to an island.
He returned by plane.
The rate of the plane was 20 times the rate of the ship.
He spent 42 hours on the trip.
Find the rate of the ship and the rate of the plane.
:
Let s = the rate of the ship
the plane is 20 times faster, therefore
20s = the rate of the plane
:
Write a time equation, time = dist/speed
Ship time + Plane time = 42 hrs
+ = 42
Multiply eq by 20s, cancel the denominators and you have
20(960) + 960 = 20s * 42
19200 + 960 = 840s
20160 = 840s
20160/840 = s
s = 24 km/hr is the rate of the ship
therefore:
20 * 24 = 480 km/hr is the rate of the plane
:
:
Check this by finding the time each way
960/24 = 40 hrs
960/480 = 2 hrs
--------------------
total time: 42 hrs

Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website!
A man traveled a distance of 960 kilometers by ship to an island. He returned by plane. The rate of the plane was 20 times the rate of the ship. He spent 42 hours on the trip. Find the rate of the ship and the rate if the plane.
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The ratio of the speeds is 20:1, so the time spent on each is 20:1 also.
42 total at 20:1 ---> 40 hours and 2 hours
Divide 960 by 40 and by 2

Answer by josgarithmetic(39799)   (Show Source):
You can put this solution on YOUR website!

SPEEDS TIME DISTANCE SHIP r 960/r 960 PLANE 20r 960/(20r) 960 TOTAL 42

Easily formulate equation and solve for r, in .

Answer by MathTherapy(10810)   (Show Source):
You can put this solution on YOUR website!
A man traveled a distance of 960 kilometers by ship to an island. He returned by plane. The rate of the plane was 20 times the rate of the ship. He spent 42 hours on the trip. Find the rate of the ship and the rate if the plane.

Let ship's speed be S Then plane's is: 20S We then get the following TIME equation: ------ Factoring out numerator-GCF, 6 160 + 8 = 7S ------ Multiplying by LCD, S 168 = 7S Ship's speed, or You should now be able to find the plane's speed.