# mathematics

posted by .

a boat travels 12 km upstream and back in 1 hour and 45 min.if the speed of the current is 3 km/h throughout,find the speed of the boat in still water,giving your answer correct to 3 decimal place.

NOTE:(Answer is 14.3 km/h,so can any one show me the solution).

• mathematics -

The speed in still water is X km/h, so the speed upstream is (X-3) km/h (slower than X because it's upstream), and the speed downstream is (X+3) km/h (faster than X because it's downstream).

Travelling at (X-3) km/h for 12 km will take 12/(X-3) hours, and travelling back again at (X+3) km/h for 12 km will take another 12/(X+3) hours.

But the whole journey takes 1.75 hours, so 12/(X-3) + 12/(X+3) = 1.75 = 7/4. We need to solve this for X. After a bit of algebraic shuffling of the above terms, we end up with 7X²-96X-63=0. One of the two solutions of this is negative and therefore impossible; the other one should be the answer you're looking for.

## Similar Questions

1. ### UPSTREAM

THIS EXURSION WITH A BOAT TRAVEL 35KM UPSTREAM AND THEN BACK AGAIN IN 4 H 48 MINUTRE. iF THE SPEED OF THE BOAT I5 K,/H, WHAT IS THE SPEED OF THE CURRENT?
2. ### Intermediate Algebra Word Problem

A river's current is 4mph. A boat travels 48 miles downstream in the same time it travels 24 miles upstream. Find the speed of the boat. A) What does the variable stand for?
3. ### Math

How do you set this up? Solve the system using substitution: A boat travels 18 miles downstream in 1.5 hrs. It then takes the boat 3 hrs. to travel upstream the same distance. Find the speed of the boat in still water and the speed
4. ### math

A boat travels 8km upstream and back in 2 hours. If the current flows at a constant speed of 3km/h, Find the speed of the boat in still water.(when the boat goes upstream, it speed reduces by 3km/h, and when going downstream, its speed …
5. ### Algebra

I am having a hard time with this question. A boat went 15 miles downstream in 1 hour and then returned upstream to its dock in 5/3 hours. if the current of the stream was constant, find the speed of the boat in still water and the …
6. ### Math

in still water, a speed boat travels 5 times faster than the current of the river. If the speed boat can travel 48 miles upstream and then back in 5 hours, find the rate of the current.
7. ### MATH

In still water, a speed boat travels 5 times faster than the current of the river. If the speed boat can travel 48 miles upstream and 10 back in 5 hours, find the rate.
8. ### Math

in still water, a speed boat travels 5 times faster than the current of the river. If the speed boat can travel 48 miles upstream and then back in 5 hours, find the rate of the current.
9. ### Algebra

A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 4 hour 30 min after first leaving N, he was brought back to N by the current. Knowing that the speed of the boat in still water …
10. ### math

A boat travels from one port A to port B, travelling 126 km, upstream (against the current) at a uniform speed, and the trip takes 6 hours.  On the way back (downstream), the trip only takes 4.5 hours. Set up and solve a system of …

More Similar Questions