I need help with a math problem and there are a lot of the similar ones, help please?

Edit:

Note firstly that the answer depends on your definition of "distance". Do you mean the distance between the start point and the end point, or the total distance upstream + total distance downstream? I assumed the former.

Lisa Dee - Sure the question is asking for the amount of TIME spent going in each direction.

distance travelled downstream = (speed downstream)*(time downstream) - (speed upstream)*(time upstream)

So,

60 = 13*(time downstream) - 7*(time upstream)

But time downstream = time upstream. So let's just represent both as "t".

Then 60 = 13t - 7t

60 = 6t

t = 10 hours

(That's 10 up, 10 down)

Given:

Ty's speed = 13m/hr down

ty's speed = 7 m/hr upstream

total distance = 60 miles

We know that:

x + y = 60 because total distance traveled is 60 miles

We also know that the time both directions is the same:

(x miles)/13mph = (y miles)/7mph

7x = 13y

From first equation, solve for x:

x miles = 60-y

Substitute into second equation and solve for y:

7(60 - y) = 13y

420 - 7y = 13y

420 = 20y

y = 21miles

x = 60 - 21 = 39 miles

CHECK SOLUTION:

7x = 13y

7(39) = 13(21)

273 = 273 -----------------------> OK

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