A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.

Question

09-06-2018
Mathematics

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A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.

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gustanika gustanika · Answer 1 · 2018-06-09T07:53:59+02:00

First, determine the distance of the motorcycle and the car from the start point. The distance could be determined using
[tex]\boxed{d=v \times t}[/tex]
d stands for distance, v stands for speed, t stands for time

The car
d = 48 × t
d = 48t

The motorcycle
d = 20 × t
d = 20t

At the end of t hours, the car is 48t miles (east) from the start point and the motorcycle is 20t miles (north) from the start point.

Second, determine the distance between 48t miles at east and 20t miles at north using pythagoras
distance = [tex] \sqrt{(48t)^{2}+(20t)^{2}} [/tex]
distance = [tex] \sqrt{2304t^{2}+400t^{2}} [/tex]
distance = [tex] \sqrt{2704t^{2}} [/tex]
distance = 52t

The expression for their distance apart at the end of t hours is 52t

fichoh fichoh · Answer 2 · 2021-09-17T19:32:25+02:00

An expression relating the distance between the car and motorcycle after t is 52t

Speed of motorcycle = 20 mph

Speed of car = 48 mph

Distance apart after, t hours :

Recall :

Distance traveled = Speed × time

Hence,

Distance traveled by car after t hours

Distance of car = 48t

Distance traveled by Motorcycle after t hours

Distance of motorcycle = 20t

Since, the direction followed by the car and motorcycle forms a right angle, the distance apart after t hours can obtained using Pythagoras :

Recall from Pythagoras :

a² = b² + c²

Where, a = hypotenus

b and c = opposite and adjacent

Therefore, distance apart :

d² = (48t)² + (20t)²

d² = 2304t² + 400t²

d² = 2704t²

Take the square root of both sides :

d = √2704t²

d = 52t

Therefore, the distance between the car and motorcycle after t hours is : 52t

Learn more : https://brainly.com/question/8283882

A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per​ hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.

Respuesta :

Otras preguntas

A motorcycle and a car leave an intersection at the same time. the motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. find an expression for their distance apart in miles at the end of t hours.