At 1:30 Marlon left his house to go to the beach, a distance of
11.25 miles. He rose his skateboard until 2:15, and then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard
2 times his walking speed. Find his speed when skateboarding and when walking.
Done here by both Steve and me
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To find Marlon's speed when skateboarding and when walking, we need to use the formula: Speed = Distance / Time.
We have the distance Marlon traveled on his skateboard, which is 11.25 miles, and the time he spent skateboarding, which is from 1:30 to 2:15 (45 minutes or 0.75 hours).
Using the formula, we can calculate Marlon's speed while skateboarding:
Skateboarding Speed = Distance / Time
Skateboarding Speed = 11.25 miles / 0.75 hours
Skateboarding Speed = 15 miles per hour
Now, let's find Marlon's walking speed. We know that he traveled the remaining distance to the beach after skateboarding, which means he traveled (11.25 - x) miles, where x represents the distance he traveled while skateboarding.
The time Marlon spent walking is from 2:15 to 3:00 (45 minutes or 0.75 hours), which is the same as the time spent skateboarding.
Using the formula, we can calculate Marlon's speed while walking after substituting the distance variables:
Walking Speed = (Distance - Distance on skateboard) / Time
Walking Speed = (11.25 miles - x miles) / 0.75 hours
Additionally, we know that Marlon's speed on the skateboard is 2 times his walking speed, so we can set up the following equation:
Skateboarding Speed = 2 * Walking Speed
Substituting the given values and solving the equation:
15 miles per hour = 2 * (11.25 miles - x miles) / 0.75 hours
Now, we can solve for x:
15 mph = 2 * (11.25 - x) / 0.75
Multiply both sides by 0.75 to eliminate the denominator:
15 mph * 0.75 = 2 * (11.25 - x)
11.25 - x = 15 * 0.75 / 2
11.25 - x = 5.625
Subtract 11.25 from both sides to isolate x:
11.25 - 11.25 - x = 5.625 - 11.25
-x = -5.625
Divide both sides by -1 to solve for x:
x = 5.625
Therefore, Marlon traveled 5.625 miles on his skateboard.
Now, let's find Marlon's walking speed by substituting the value of x into the earlier equation:
Walking Speed = (11.25 miles - x miles) / 0.75 hours
Walking Speed = (11.25 miles - 5.625 miles) / 0.75 hours
Walking Speed = 5.625 miles / 0.75 hours
Walking Speed = 7.5 miles per hour
So, Marlon's speed on his skateboard is 15 miles per hour, and his walking speed is 7.5 miles per hour.