Question

Car A leaves San Diego at noon driving at 60 mph along a route which is 400 miles long to San Francisco. Car B leaves San Francisco 2 hours later traveling along the same route at 80 mph. How far from the midpoint of the route are they when they meet? Are they closer to San Diego?

This is my question and I don't get what I'm supposed to do.. I don't know when they meet I'm not sure where to put the variables either.

Answer 1

After solving the equation for the time when Car A and Car B meet, we find that they are 40 miles from the midpoint when they meet, which is closer to San Francisco.

Step-by-step explanation:

To solve this problem, we need to set up an equation to determine when Car A and Car B will meet. Let's denote t as the time after Car A leaves San Diego when the two cars meet. Because Car A has a 2-hour head start, Car B will have been traveling for t-2 hours by the time they meet.

Car A's distance traveled can be represented as DistanceA = 60 mph × t. Similarly, Car B's distance traveled can be DistanceB = 80 mph × (t - 2). When they meet, the sum of these two distances will be equal to the total distance between San Diego and San Francisco, which is 400 miles. So, we have the equation: 60t + 80(t - 2) = 400.

Solving this equation will give us the value of t. We can then calculate DistanceA to find where Car A is when they meet. The midpoint of the route is at 200 miles from San Diego. By subtracting Car A's distance from 200 miles, we'll know how far from the midpoint they are when they meet.

Now, let's solve the equation:

• 60t + 80(t - 2) = 400
• 60t + 80t - 160 = 400
• 140t = 560
• t = 4

So, they meet 4 hours after Car A leaves San Diego. Car A's distance is 60 mph × 4 h = 240 miles. The midpoint is at 200 miles, so they are 240 - 200 = 40 miles from the midpoint when they meet, closer to San Francisco since they have traveled past the midpoint.

Answer 2

Distance = speed x time
Distance travelled by car A when car B started = 60 x 2 = 120 miles
Number of miles remaining at the time car B started = 400 - 120 = 280 miles.

At time of their meeting both cars has travelled a combined distance of 280 miles and has spent the same time.
Let t be the time they travelled together before they meet, then the sum of the distance travelled by car A and car B is 280miles.
60t + 80t = 280
140t = 280
t = 280/140 = 2 hours

After 2 hours car A has travelled a further 60 x 2 = 120 miles and car B has travelled 80 x 2 = 160 miles.

Total distance travelled be car A is 120 + 120 = 240 miles

Midpoint of the journey = 400/2 = 200 miles
Therefre, at the time they met, the were 40 miles from the midpoint and they are close to San Francisco.