# Point A and B are 200 mi apart.A cyclist starting at a point A and a motorcyclist at a point B moves toward each other.The speed of the cyclist is 17 mph, and the speed of motorcyclist is

Step By Step Solution:

Let t be a time when cyc and mo meet:

The distance between points A and B is 200mi:

Let d1 be the distance covered by cyc from point A:

Recall the Speed:

Speed=\frac{Distance}{Time}
17~mph=\frac{d{1}}{t}\implies d_1=17t

Find the d1:

d1=17t

Let d2 be the distance covered by mo from point B:

Recall the Speed:

83~mph=\frac{d{2}}{t}\implies d_2=83t

Find the d2:

d2=83t

Points A and B are 200~mi apart:

It means,

d{1}+d{2}=200

Substitute the

d_1=17t, d_1=83t

into the above:

Simplify the expression:

17t+83t=200\implies 100t=200

Find the t:

100t=20 \implies t=2

Find the d1 for t=2:

d1=17t\implies d_1=17\times 2\implies d_1=34

Therefore, The 34 miles distance from point A will they meet:

34 miles distance from point A will they meet

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