Question

The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:


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Car A

y = 55x + 32


Car B

y = 42x + 58

After how many hours will the two cars be at the same distance from their starting point and what will that distance be?

2 hours, 142 miles

2 hours, 145 miles

3 hours, 142 miles

3 hours, 145 miles

Answer 1

Answer:

2 hours, 142 miles

Step-by-step explanation:

Given;

equation of motion of car A as;

y = 55x + 32

equation of motion of car B as;

y = 42x + 58

where;

y is distance measured in miles

x is time measured in hours

When the distance of the two cars are equal, we will have the following equation;

55x + 32 = 42x + 58

collect like terms and solve for x

55x - 42x = 58 - 32

13x = 26

x = 26 /13

x = 2 hours ( x is time measured in hours)

Now substitute in the value of x into any equation of the cars;

y = 55x + 32

y = 55 (2) + 32

y = 110 + 32

y = 142 miles ( y is distance measured in miles)

Thus, the correct option is 2 hours, 142 miles