Question

Bob leaves school at the same time as Jane. Bob drives 4 mph faster than Jane. After 2 hours of driving in opposite directions, they are 116 miles apart. Let B represent the speed that B is driving so B-4 is Jane's speed.does this equation work 2(B+B - 4) = 116 O True O False

Answer 1

Let the bob's speed be represented below as

`=b`

Since bob drives 4mph faster than jane, janes, speed will be represented below as

`jane=b-4`

The total speed will be calculated below as

`b+b-4`

The time taken is given below as

`=2hrs`

The total distance apart is given below as

`=116mi`

Concept:

Using the formula below, we will have

`distance=speed* time`

By substituting the values, we will have

`\begin{gathered} distance=2(b+b-4) \\ 2(b+b-4)=116 \end{gathered}`

By simplifying further, we will have

`\begin{gathered} 2(b+b-4)=116 \\ 2(2b-4)=116 \\ 2b-4=(116)/(2) \\ 2b-4=58 \\ 2b=58+4 \\ (2b)/(2)=(62)/(2) \\ b=31mi\text{ }per\text{ }hr \end{gathered}`

Substitute b=31 in the equation below

`\begin{gathered} jane=b-4 \\ jane=31-4 \\ jane=27\text{ }mi\text{ }per\text{ }hr \end{gathered}`

Hence,

Jane is driving at 27 miles per hour

Bob is driving at 31 miles per hour

The final answer is TRUE