Question

A boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h. What is the boat's speed (in still water)?

Answer 1

The boat's speed in still water is calculated as 63 miles/hour. This is derived by setting up equations for the boat's journey downstream and upstream, and solving for the boat's speed by adding both equations.

Step-by-step explanation:

To solve this problem, we need to make use of the formula for speed, which is distance divided by time. On the trip downstream, we know that the boat travels 90 miles in 1 hour, giving it a speed of 90 miles/hour. When traveling upstream against the current, the boat covers the same distance, but in 2 1/2 hours, giving it a speed of 36 miles/hour.

However, when the boat is traveling downstream, its speed is actually the sum of its speed in still water, and the speed of the current (since it's being helped by the current). Conversely, when the boat is making its journey upstream, its effective speed is the difference between its speed in still water, and the speed of the current (since it's being impeded by the current).

We can set up two equations to represent this situation:

1) Boat speed in still water + Current speed = 90 miles/hour (downstream speed)

2) Boat speed in still water - Current speed = 36 miles/hour (upstream speed)

To find the boat's speed (in still water), we simply add these two equations. This will give us: 2 x Boat speed in still water = 90 miles/hour + 36 miles/hour = 126 miles/hour. Thus, the boat's speed in still water is 126 miles/hour divided by 2, which equals 63 miles/hour.

Learn more about Boat speed

Answer 2

A)63miles per hour.

B)27 miles per hour

Step-by-step explanation:

HERE IS THE COMPLETE QUESTION

boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h. What is the boat's speed (in still water)??b) How fast does the current in the river flow?

Let the speed of boat in still water = V(boat)

speed of current=V(current)

To calculate speed of boat downstream, we add speed of boat in still water and speed of current. This can be expressed as

[V(boat) +V(current)]

It was stated that it takes 1hour for the

boat to travels between two points of 90 mi apart downstream.

To calculate speed of boat against current, we will substact speed of current from speed of boat in still water. This can be expressed as

[V(boat) - V(current)]

and it was stated that it takes 2 1/2 for return trip against the Current

But we know but Speed= distance/time

Then if we input the stated values we have

V(boat) + V(current)]= 90/1 ---------eqn(1)

V(boat) - V(current) = 90/2.5----------eqn(2)

Adding the equations we have

V(boat) + V(current) + [V(boat) - V(current)]= 90/2.5 + 90/1

V(boat) + V(current) + V(boat) - V(current)]=90+36

2V(boat)= 126

V(boat)=63miles per hour.

Hence, Therefore, the speed of boat in still water is 63 miles per hour.

?b) How fast does the current in the river flow?

the speed of the current in the river, we can be calculated if we input V(boat)=63miles per hour. Into eqn(1)

V(boat) + V(current)]= 90/1

63+V(current)=90

V(current)= 27 miles per hour

Hence,Therefore, the speed of current is 27 miles per hour.