Question

Please please please help I cannot figure this problem out

Car A is traveling east at a steady speed of 60 miles per hour after 2 hours, it is 130 miles east of Johnstown. car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.

Answer 1

45 mph = x

Explanation:

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Distance (D) = Rate (R) * Time (T)

For Car A:

D = 30T {Eqn 1}

For Car B:

The Distance D and the time T is the same as for Car A

But, unlike Car A, Car B travels at two different rates. It travels at 20mph for a time T1. Then it passes Car A and travels at a rate of x for a period of time T2.

D = (20T1) + (x * T2)

Note that T2 must equal the total time T minus T1, so

D = (20T1) + (x * (T - T1)) {Eqn2}

Substitute Eqn 1 into Enq 2 : 30T = 20T1 + xT - xT1

Rewrite as: 30T = 20T1 + x(T-T1) {Eqn 3}

At what point do the two cars pass one another?

Car A travels 30T1 = D1

Car B is traveling in the opposite direction at 20T1 = D2

D2 = D - D1 (where D is the total circular length of the track)

Substituting, 20T1 = D - 30T1. Or 50T1 = D {Eqn 4}

Now we can establish a relationship between T and T1 by substituting Eqn1 into Eqn4

D = 30T = 50T1

30T = 50T1

(30/50)T = T1

T1 = (3/5)T {Eqn 5}

Now substitute Eqn 5 into Eqn 3

30T = 20T1 + x (T-T1)

30T = 20(3/5)T+ x (T - 3/5 T)

30T = 12T + xT(2/5)

18T = (2/5)x

(5/2)18 = x

45 mph = x

Recall that x is the speed that Car B must travel after it passes Car A.