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For a ship moving against the current, it takes 9 hours to cover a distance of 113.4 miles. How much does it take this ship to return if the rate of the current is 1.9 mph?


Two trains move between two towns. It takes the first train 2 hr 48 min and it takes the second 4 hr 40 min. The rate of the first train is 26 mph more than that of the second train. What is the distance between these towns?
Apr 10th, 2015

1.  Let  x = speed of the ship without current

Then, moving against the current

x - 1.9 = 113.4/9

x - 1.9 = 12.6

x = 14.5 mph

moving with the current the ship's speed is 14.5 + 1.9 = 16.4mph

therefore the time it takes to return is

113.4/16.4 = 6.9 hours

2.  Let x = rate of the first train

Let y = rate of the second train

then, x = y + 26

distance = (rate)(time)

For the first train

distance = 2.8x

For the second train

distance= 4.67y

but both distances are the same, so

2.8x = 4.67y

Now substitute x for y+26

2.8(y+26) = 4.67y

2.8y + 72.8 = 4.67y

1.87y = 72.8

y = 38.93 mph

so, the distance = (38.93)(4.67) = 181.8 miles

Apr 10th, 2015

Hey, umm, sorry, but the second one wasnt right. Could you do it again? Thanks, and sorry for all the hassle 

Apr 10th, 2015

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