Find the speed of the current and each girls rowing speed

Question

 Emily rows  6 miles downstream in one hour and her friend Ashley, rowing 1 mph faster completes the return trip in two hours.

 

 Find the speed of the current (c)  and each girls rowing speed. 

Answer 1

Hello, Jack:

Questions like these appear to be super tricky, but we can use algebra to find their answers.

First of all, we know the values we need to find: the speed of the current, c, as well as each girl's rowing speed. Let's call Emily's speed e. We'll call Ashley's speed e + 1 since she rowed 1 mile per hour faster than Emily did. We're off to a good start!

Since we know the distance the girls rowed, we can use the equation d = rt (distance equals rate multiplied by time) to find out the speed of the current and the girls' rowing speeds.

Now let's look at the algebra that will give us the values we need.

Step one: Set up the equations

1. Since d = rt, and we know the distance and the amounts of times the girls traveled, we can set up two equations:
2. 6 = 1 (e + c)
3. 6 = 2 ( e + 1 - c)
4. Let's make sure we know what those equations mean!
5. 6 = 1 (e + c) means that in 1 hour, Emily rowed six miles, and the current increased her overall speed.
6. 6 = 2 ( e + 1 - c) means that in 2 hours, Ashley rowed six miles, and the current decreased her overall speed.

Step two: Do the algebra.

1. We'll use the two equations to solve for e. Once we know e, we can figure out the other values.

Again, the equations are:

1. 6 = 1 (e + c)
2. 6 = 2 ( e + 1 - c)
3. Let's first simplify those, by multiplying the equations in parentheses by the number outside the

parentheses.

1. 6 = 1 (e + c) → 6 = e + c

6 = 2 ( e + 1 - c) → 6 = 2e + 2 - 2c → 4 = 2e - 2c

1. Then, we can add the simplified equations to isolate the variable e.

First, we need to multiply the first equation by 2 so that we will be adding 2c to -2c; this will eliminate

the variable c.

1. 6 = e + c → 2(6) = 2(e + c) → 12 = 2e + 2c

4 = 2e - 2c

1. 12 = 2e + 2c

+

4 = 2e - 2c

16 = 4e + 0

1. Since 4e = 16, if we divide both sides of the equation by 4, we get the value of 4 for e.

Step two: Use the value of e to solve for the other values.

1. We know that Emily rowed at a speed of 4 mph, and that she rowed 6 miles downstream in an hour. We can use this information to find the speed of the current: our first equation has as its variables Emily's speed, e, and the speed of the current, c:
2. 6 = 1 (e + c)
3. Substitute 4 for e, and we get:
4. 6 = 4 + c
5. Subtract 4 from both sides of the equation, and we get 2 as the value for c.
6. Ashley's speed is just 1mph greater than Emily's (e + 1), so it is 5 mph, or 5.

Step three: Check your work by substituting the values into the equations.

1. 6 = 1 (e + c) → 6 = 4 + 2 → 6 = 6 ✓
2. 6 = 2 ( e + 1 - c) → 6 = 2(4 + 1 -2) → 6 = 2(5 - 2) → 6 = 6 ✓

Emily's rowing speed was 4mph, Ashley's was 5mph, and the current was 2mph.

In conclusion: The problem appears tricky at first, but once we know what the problem is asking, we can use our knowledge of algebra to find those answers!