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At 1:30 Marlon left his house to go to the beach, a distance of 6.3 miles. He rode his skateboard until 2:15, then walked the rest of the way. He arrived at the beach at 3:00. Marlon's speed on his skateboard is 2.5 times his walking speed. Find his speed, in miles per hour, when skateboarding and when walking.

Respuesta :

joseaaronlara

Answer:

The answer to your question is speed when skating = 6 mi/h; when walking = 2.4 mi/h

Step-by-step explanation:

Data

Total time = 1:30 h

total distance = 6.3 mi

time in skateboard = 2:15 - 1:30 = 45 min

time walking = 3:00 - 2:15 = 45 min

Speed skating is 2.5 faster than walking

Process

1.- Let x be the speed when walking

    speed when skating = 2.5x

2.- Use the formula of velocity to find x

Walking     x = d1/t      or    d1 = xt

Skating      2.5x = d2/t   or   d2 = 2.5xt

Total distance =    d1 + d2 = 6.3

                               xt + 2.5xt = 6.3

- Solve for x           3/4x + 2.5(3/4)x = 6.3

-Simplification      3/4x + 15/8x = 6.3

                              21/8x = 6.3

                                     x = 2.4

3.- Find the speed when skating

Speed when skating = 2.5(2.4)

                                  = 6                              

Answer: his walking speed is 2.4 mph.

His skateboarding speed is 6 mph.

Step-by-step explanation:

Let x represent Marlon's walking speed.

Marlon's speed on his skateboard is 2.5 times his walking speed. It means that his speed on his skateboard is 2.5x.

At 1:30 Marlon left his house to go to the beach, a distance of 6.3 miles. He rode his skateboard until 2:15. This means that he spent 45 minutes (45/60 = 0.75 hour) on the skateboard.

Distance = speed × time

Distance covered while skateboarding is

0.75 × 2.5x = 1.875x

He walked the rest of the way. He arrived at the beach at 3:00. This means that he spent 45 minutes (45/60 = 0.75 hour) walking. Distance covered while walking is

0.75x

Since the total distance covered is 6.3 miles, then

1.875x + 0.75x = 6.3

2.625x = 6.3

x = 6.3/2.625

x = 2.4 mph

His speed while skateboarding is

2.4 × 2.5 = 6 mph

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