Question

A straight road connects the towns of Winridge and Upper Lansbury are (6,10). If Ty drives from Winridge to Upper Lansbury at an average speed of 40 miles per hour, will the trip take more than an hour? Explain

Answer 1

The trip will take more than one hour

Explanation:

The complete question is

A straight road connects the towns of Winridge and Upper Lansbury. On a map on which each unit represents 10 miles, the coordinates of Winridge are (8,4) and the coordinates of Upper Lansbury are (6,10). If Ty drives from Winridge to Upper Lansbyet at an average speed of 40 miles per hour, will the trip take more than an hour? Explain your reasoning

we know that

The speed is equal to divide the distance by the time

so

s=d/t

Solve for t

t=d/s ----> the time is equal to divide the distance by the speed

step 1

Find the distance

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have

(8,4), (6,10)

substitute

`d=\sqrt{(10-4)^(2)+(6-8)^(2)}`

`d=\sqrt{(6)^(2)+(-2)^(2)}`

`d=√(40)`

`d=2√(10)\ units`

Convert to miles

`d=2√(10)*10=20√(10)\ miles`

`d=63.2\ miles`

step 2

Find the time

we have

s=40 miles/hour

d=63.2 miles

t=d/s -----> t=63.2/40=1.58 hours

1.58 hours > 1 hour

therefore

The trip will take more than one hour