Question

Please help!! Its important!
Solve using substitution!
A jet boat is used to take canoers 200 miles upriver to their starting point. As the driver of the jet boat, Jeremy knows that it will take him 5 hours to get the canoers upstream, but only 4 hours to get the boat back downstream after dropping the canoers off, as long as he keeps the boat moving at a constant speed.

How fast would the boat be moving in still water?
A.
5 mph
B.
40 mph
C.
45 mph
D.
50 mph

Answer 1

Let speed of boat in still water is x miles/hr
and speed of river is y miles/hr.
so upstream, speed of boat=(x-y) miles/hr
downstream, speed of boat=(x+y) miles/hr

Answer 2

now. we know
Distance= speed*time
so upstream, 200=(x-y)5
i.e., 5x-5y=200

Downstream,
200=(x+y)4
i.e., 4x+4y=200
now solve the two equations by any method you know to solve equations of two variables to find x and y.
x is the speed of boat in still water.
and y is the speed of stream or river.

Answer 3

Thank you so much! This is so helpful. I was so stuck. Work problems aren't my thing.

Answer 4

nvm... you're welcome..:)

Answer 5

No no, continue. I still need help. XD

Answer 6

5x-5y=200......(i)
4x+4y=200......(ii)
multiply (i) with 4 and (ii) by 5 and add both.

Answer 7

u can also take the 200 miles divide it by 5 hrs and get 40 (the going trip) which is mph then divide 200 miles by 4 hrs and get 50 (the return trip)mph the add 40+50 =90mph for the total trip and divide by 2 to get the average of 45mph

Answer 8

the way @neer2890 did it is correct also!

Answer 9

yeah... but adopt the method used by @sneakergyrl when you understand the previous one.. because it's a shortcut.