Question

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8.06 MC)

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

Car A:
y = 52x + 70

Car B:
y = 54x + 56

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

6 hours, 420 miles
6 hours, 434 miles
7 hours, 420 miles
7 hours, 434 miles

Answer 1

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

`\begin{gathered} y\text{ = 52x + 70 }\ldots\ldots\ldots.car\text{ A} \\ y\text{ = 54x + 56 }\ldots\ldots\ldots..car\text{ B} \end{gathered}`

Two cars be at the same distance when car A = car B

`\begin{gathered} 52x\text{ + 70 = 54x + 56} \\ \text{collect like terms} \\ 52x\text{ - 54x = 56 - 70} \\ -2x\text{ = -14} \\ \text{divide both side by -2} \\ x\text{ = }(-14)/(-2) \\ x\text{ = 7} \end{gathered}`

The two cars will be at same distance at 7 hours

`\begin{gathered} \text{For Car A} \\ y=52x\text{ + 70 when x = 7hours} \\ y=52(7)\text{ + 70} \\ y=364\text{ + 70} \\ y=434\text{ miles} \end{gathered}`

The distance covered = 434 miles

Hence the hours and distance covered are 7hours , 434 miles