Question

Sheila and Lenore were driving to their grandmother’s house. Lenore left 1 hour after Sheila. Sheila drove at a rate of 45mph, and Lenore drove at a rate of 60mph. How long will it take for Lenore to catch up to Sheila?

Answer 1

Lenore will take 3 hours to catch up to Sheila.

Step-by-step explanation:

To determine how long it will take for Lenore to catch up to Sheila, we can set up an equation based on their speeds and the time difference. Let's denote the time it takes for Lenore to catch up to Sheila as t. Since Lenore left 1 hour after Sheila, Sheila would have already traveled for t + 1 hours when Lenore starts driving.

Sheila's distance = speed * time = 45 * (t + 1)

Lenore's distance = speed * time = 60 * t

Since they will meet at the same distance, we can set up the equation: 45(t + 1) = 60t

Simplifying the equation, we get: 45t + 45 = 60t

Subtracting 45t from both sides, we get: 45 = 15t

Dividing both sides by 15, we get: t = 3

Therefore, it will take Lenore 3 hours to catch up to Sheila.

Answer 2

It'll take 3 h before Lenore catch up to Sheila.

Step-by-step explanation:

To solve this problem we first need to calculate the relative speed between the two. Since they're going at the same direction we need to subtract their individual speeds if their directions were oposite we would have to sum their speeds. In this case we have:

relative speed = Lenore speed - Sheila speed

relative speed = 60 - 45 = 15 mph

Since Sheila left 1 h before Lenore and she drove at a rate of 45 mph, then she had covered a distance of:

distance = time*speed = 1*45 = 45 miles

Before Lenore left, so in order for Lenore to catch up to Sheila she needs to cover that distance at a relative speed of 15 mph.

time = distance/(relative speed) = 45/15 = 3 h

It'll take 3 h before Lenore catch up to Sheila.