Math help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!?

Question

A speedboat could travel at 4 times the speed of the current. Thus, it could travel 700 miles downriver in 2 hours more than it took to travel 400 miles upriver. What was the speed of the boat in still water.

plz use a system of equations and explain thoroughly

Answer 1

Let r = the rate of the current. Then 4r = the boat's speed in still water. If t is the time going downriver (with the current) the speed would be 4r + r = 5r, and distance = rate times time, so

700 = 5rt

Upriver, the time was t-2, the speed was 4r - r = 3r, and the distance was 400, so

400 = 3r(t-2) = 3rt - 6r

Multiply the first equation by 3 and the second by -5 then add together to eliminate the rt term. leaving just r. Then solve for r.

Answer 2

When doing "stream" word problems like this, the thing to keep in mind is that a boat traveling downstream is being pushed along by the current, but traveling upstream the boat has to work against the current. More specifically, a boat going downstream is going to be traveling at the same speed it would be going if it were apply the same power in still water, PLUS the speed of the stream. Going upstream, the boat's overall speed would be the speed if there was no current, MINUS the speed of the steam.

Honestly, I think this problem is badly worded. The first sentence could mean either the boat travels 4 times the speed of the current as it's going downstream (which is when the boat would be the fastest) or in still water (when it's just the boat moving on its own). Let C be the speed of the current, and B be the speed of the boat in still water. Then...

1) If the speed of the boat going downstream is 4 times the speed of the current, then (B+C)=4C. You're then told how far the boat could travel upstream and downstream in certain amounts of time. Speed times time euqals distance, so if "t" is the amount of time it took to go downstream, (B+C)t = 700.

We're told it traveled this in two hours MORE than it took to travel 400 miles upstream. I thought this was strange, because you'd think they'd want to compare distances by showing how going downstream SAVES you time. I tried calculating it out and got a negative value for C, so my guess is that they probably worded the problem wrong, and meant to say "in 2 hours less than [traveling upstream]. So if it took two hours more than t to go 400 miles upstream, then (B-C)(t+2) = 400.

You've got 3 equations with 3 unknowns. So solve it for B. I got 37.5 miles per hour:
B+C=4C
(B+C)t = 700
(B-C)(t+2) = 400

2) If the first sentence is referring to the speed of the boat in still water, then B=4C. If we assume the rest of the wording is right (the time measured downstream was more than the time measured upstream), then we get
B=4C
(B+C)t = 700
(B-C)(t-2) = 400
Again, solve 3 equations for 3 unknowns.

Answer 3

Current speed = x
Boat speed = 4x
Time = t

Distance = Speed * Time

Going downriver,
(4x + x) * t = 700;
5x * t = 700
t = 140/x

Going upriver,
(4x - x) * (t - 2) = 400;
3x * (t - 2) = 400;
t-2 = 400/3x
t = (400/3x)+2

Setting one equal to the other,

140/x = (400/3x)+2
420 = 400 + 6x
20 = 6x
x = 10/3 mph

So the current goes 3 1/3 mph; and the boat goes 4 times as much, or 13 1/3 mph. It goes downriver at 16 2/3 mph, traveling 700 miles in 42 hours. Upriver, it can only make 10mph, traveling 400 miles in 40 hours.

Hope that helps.

Answer 4

x = speed of current
So 4x = speed of boat
Speed upstream 4x-x = 3x
Speed downstream = 4x+x = 5x
time upstream = 400/3x
time downstream = 700/5x
700/5x -400/3x =2
2100/15x-2000/15x = 2
100/15x = 2
100 = 30x
x= 3 1/3 mph = speed of current
4x =13 1/3 mph = speed of boat in still water