In a bike race, bike A is 50 miles from the starting point and travels 30 miles per hour. Bike B is 100 miles from the starting point and travels 25 miles per hour. After how many miles will bike A and bike B be the same distance from the starting point?(1 point)

Answer 1

To figure out when Bike A and Bike B will be the same distance from the starting point, we need to determine when they will have covered the same distance.
Let's consider the time it takes for both bikes to reach the same distance from the starting point.

For Bike A:
We can use the formula distance = rate x time.
Given that Bike A is 50 miles from the starting point and travels at a speed of 30 miles per hour, we can set up the equation:
50 = 30 * time_A

For Bike B:
Given that Bike B is 100 miles from the starting point and travels at a speed of 25 miles per hour, we can set up the equation:
100 = 25 * time_B

Now, let's solve the equations simultaneously to find when the two bikes will be the same distance from the starting point.

From the equation for Bike A, we can solve for time_A:
time_A = 50/30 = 5/3 hours

From the equation for Bike B, we can solve for time_B:
time_B = 100/25 = 4 hours

Since Bike A will take 5/3 hours and Bike B will take 4 hours to reach the same distance from the starting point, we need to know how far each bike has travelled in those time intervals.

For Bike A:
distance_A = rate_A * time_A = 30 * 5/3 = 50 miles

For Bike B:
distance_B = rate_B * time_B = 25 * 4 = 100 miles

Therefore, Bike A will travel 50 miles and Bike B will travel 100 miles in the given time intervals.
So, Bike A and Bike B will be the same distance from the starting point after traveling 100 miles.

Answer 2

Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?(1 point)

Answer 3

To determine when the two vats will have the same amount of liquid, we need to set up an equation based on the rates at which the liquid is being added to each vat.

Let's consider the time it takes for both vats to have the same amount of liquid.

For the empty vat:
The pump is filling it at a rate of 6 gallons per minute.

For the vat with 28 gallons:
The liquid is added at a rate of 4 gallons per minute.

Let's denote the time it takes for the two vats to have the same amount of liquid as t minutes.

For the empty vat, the amount of liquid in t minutes would be 6t gallons.
For the vat with 28 gallons, the amount of liquid in t minutes would be 28 + 4t gallons.

Setting these two equations equal to each other, we have:
6t = 28 + 4t

Simplifying the equation:
2t = 28

Solving for t:
t = 28/2 = 14 minutes

Therefore, after 14 minutes, the two vats will have the same amount of liquid.