Mason starts walking from home at 3.7 mph. Ema leaves to follow Mason 48 minutes later walking at 4.1 mph. How long will it take Ema to catch up to Mason?

RT = D (rate * time = distance)

4.1 = Emma's rate
3.7 = Mason's rate
T = Emma's time
T + .08 = Mason's time (48/60 = 0.8h)
4.1T = Emma's distance
3.7(T + 0.8) = Mason's distance

Distances are equal to each other
3.7(T + 0.8) = 4.1T
3.7T + 2.96 = 4.1T
0.4T = 2.96
T = 7.4 hour

Emma will catch up to Mason in 7.4 hours

To find out how long it will take Ema to catch up to Mason, we need to first determine how far Mason walks in 48 minutes.

We know that the formula to calculate distance is: Distance = Speed × Time.

Given that Mason walks at a speed of 3.7 mph, we can convert 48 minutes into hours by dividing it by 60 (since there are 60 minutes in an hour): 48 minutes ÷ 60 = 0.8 hours.

Now we can calculate the distance Mason covers in 48 minutes: Distance = Speed × Time = 3.7 mph × 0.8 hours = 2.96 miles.

Since Ema starts walking 48 minutes later, she needs to cover the same distance as Mason to catch up. Now we can set up an equation to solve for the time it will take Ema to catch up to Mason:

Distance covered by Ema = Speed of Ema × Time taken by Ema

Given that Ema walks at a speed of 4.1 mph, and we know the distance covered by Ema is 2.96 miles, we can rearrange the equation to solve for time:

Time taken by Ema = Distance covered by Ema ÷ Speed of Ema = 2.96 miles ÷ 4.1 mph

Calculating this equation will give us the time it takes Ema to catch up to Mason.