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.

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                              

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

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4