Question

Points A and B are 200 mi apart. A cyclist started from point A and a motorcyclist started from point B, moving towards each other.The speed of the cyclist was 17 mph, the speed of motorcyclist was 83 mph. At what distance from point A will they meet?

Answer 1

Answer:

34 miles is the distance from point A will they meet.

Step-by-step explanation:

Proportion states that the two ratios or fractions are equal.

Given the statement:

Distance between point A and B (i.e AB) = 200 mi.

Let the cyclist speed be c, and motor- speed be m;

then;

c = 17 mph and m=83 mph

Let they meet at distance x miles from a point A.  

By definition of proportion, we have;

$\frac{x}{17} =\frac{200-x}{83}$

By cross multiply;

$83x = 17(200-x)$

Using distributive property, $a\cdot(b+c) =a\cdot b+ a\cdot c$

$83x = 3400 - 17x$

Add 17x both sides we get;

$83x+ 17x= 3400 - 17x +17x$

Simplify:

100x = 3400

Divide by 100 on both sides we get;

x = 34 miles

Therefore, the distance from point A will they meet is, 34 miles.