Question

Two cyclists start from the same location. One cyclist travels due north and the other due east, at the same speed. Find the speed of each in miles per hour if after two hours they are 17sqrt(2) miles apart

Answer 1

Explanation:

1. Determine whether the word problem can be modeled by a right triangle.

2. Use the Pythagorean Theorem to find the missing side if you are given two sides.

Example:

Shane marched 3 m east and 6 m north. How far is he from his starting point?

Solution:

First, sketch the scenario. The path taken by Shane forms a right-angled triangle. The distance from the starting point forms the hypotenuse.

Answer 2

Given:

Distance between the first cyclist and the second cyclist = 17√2 miles

To find:

Speed of each cyclist.

Solution:

One cyclist is travelling due north and the other cyclist is travelling due east which is in the perpendicular direction of north. They are 17√2 miles apart after cycling for 2 hours. Hence, the cyclists are at the endpoints of a right-angled triangle whose hypotenuse is given by the distance between them as shown in the figure.

Since, they are travelling with the same speed, the distance they travelled in 2 hours is also same.

Let the distance travelled by each cyclist be $x$.

By Pythagoras theorem,

$NE^{2}=ON^{2}+OE^{2}$

$(17\sqrt{2})^{2}=x^{2} +x^{2}$

$578=2x^{2}$

$x^{2} =\frac{578}{2}=289$

$x=17miles$

Distance covered by the cyclists in 2 hours is 17 miles. To calculate speed of each cyclist, we use the formula:

$Speed=\frac{Distance}{Time}$

$Speed=\frac{17}{2}=8.5miles/hour$

Hence, the speed of each cyclist is 8.5 miles/hour.

The speed of each cyclist is 8.5 miles/hour.