# Algebra

A riverboat cruise line has a boat that can travel 76 mi downstream in the same time that it takes to travel 52 mi upstream. The speed of the current in the river is 1.5 mph. Find the speed of the boat in still water.

1. 👍 0
2. 👎 0
3. 👁 368
1. speed of boat in still water ---- x mph
speed against current = x-1.5
speed downstream = x+1.5

time to go 75 miles downstream = 75/(x+1.5)
time to go 52 miles upstream = 52/(x-1.5)

so 75/(x+1.5) = 52/(x-1.5)
cross-multiply and solve for x

1. 👍 0
2. 👎 0
76x - 114 = 52x + 78
24x = 192
x = 8

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Physics

A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.35 km/hr. The child is 0.625 km from shore and 0.800 km upstream of a boat landing when a rescue boat sets out. If the boat

2. ### physics

A boat travels at 3.8 m/s and heads straight across a river 240 m wide. The river flows at 1.6 m/s. Find A) The boat's resultant velocity. B) How long it takes the boat to cross the river. C) How far downstream the boat is when it

3. ### Science

A boat moves at a speed of 15 km/h in still water. The river it is traveling in flows at a rate of 3 km/h downstream. What is the velocity of the boat if it travels downstream? What is the velocity of the boat if it travels

4. ### Physics

A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.60km/h. The child is 0.615km from shore and 0.815km upstream of a boat landing when a rescue boat sets out. If the boat

1. ### phy

A boat can travel 2.60 m/s in still water.If the boat points its prow directly across a stream whose current is 1.10 m/s, what is the velocity (magnitude and direction) of the boat relative to the shore? What will be the position

2. ### Physics

A child in danger of drowning in a river is being carried downstream by a current that has a speed of 2.60km/h. The child is 0.565km from shore and 0.790km upstream of a boat landing when a rescue boat sets out. If the boat

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

4. ### physics

A boat can travel at a speed of 8km/h in still water on a lake.In flowing water of a stream, it can move at 8km/h relative to the water in the stream.If the stream speed is 3km/h, how fast can the boat travel upstream and

1. ### Math (Trig.)

A boat sailing from A to B travels in a straight line until the captain realizes he is off course. The boat is turned through an angle of 60 degrees, then travels another 10 km to B. The trip would have been 4 km shorter if the

2. ### physics

A riverboat travels with a velocity of 4.60 m/s from one shore to another. The velocity of the river is 2.30 m/s. If the width of the river is 72.0 m, how far does the boat travel downstream to reach the other shore?

3. ### Math

It takes a boat 2 hours to travel 26 miles downstream and 4 hours to travel 28 miles upstream.

4. ### Physics

A motorboat heads due east at 8.5 m/s across a river that flows to the south at a speed of 2.5 m/s. a. What is the velocity of the boat relative to a stationary observer on the shore? B. If the river is 1360 m wide, how long does