Question

Susan drove 1500 miles to Daytona Beach for spring break.On the way back she averaged 10 miles per hour less, and the drive back took her 5 hours longer . Find Susan's average speed on the way to Daytona Beach.

Answer 1

By setting up an equation based on time and distance, and solving for x, we find Susan's average speed on the way to Daytona Beach was 60 mph.

Step-by-step explanation:

To find Susan's average speed on the way to Daytona Beach, we can set up an equation based on the information provided. Let's assume her average speed on the way to Daytona Beach is x miles per hour (mph). This means her average speed on the way back was x - 10 mph. Since distance is the same in both directions, we can use the formula time = distance/speed.

On the way to Daytona Beach, the time taken would be 1500/x hours. On the way back, it would be 1500/(x - 10) hours. We are given that the trip back took 5 hours longer, so we can set up the following equation:

1500/(x - 10) - 1500/x = 5

Solving this equation will give us Susan's average speed to Daytona Beach. To do this, we find a common denominator and solve for x:

1. Multiplying both sides by x(x - 10) to clear the fractions, we get:
2. 1500x - 1500(x - 10) = 5x(x - 10)
3. This simplifies to:
4. 15000 = 5x^2 - 50x
5. Divide by 5:
6. 3000 = x^2 - 10x
7. Rearrange:
8. x^2 - 10x - 3000 = 0
9. Factor the quadratic equation:
10. (x - 60)(x + 50) = 0
11. Since speed can't be negative, x = 60 mph

Susan's average speed on the way to Daytona Beach was 60 mph.

Answer 2

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