Question

Jenny, who rides a moped, takes 2 hours less to travel 60 miles than Maureen takes to travel 50 miles on her bicycle. Jenny travels 10 miles per hour faster than Maureen. (Hint: speed = distance ÷ time.)

Answer 1

Jenny

`d_(Jenny)=60mi`

`t_(Jenny)=x-2`

Speed is defined by:
`s=(d)/(t)`, which in this case is
`s=(60)/(x-2)`

Maureen

`d_(Maureen) =50mi`

`t_(Maureen)=x`

Her speed would be
`s=(50)/(x)`

We know that Jenny travels 10 miles per hour faster than Maureen, in other words, the difference between their speeds is 10 miles per hour, which can be expressed as

`Jenny - Maureen = 10mph\\(60)/(x-2)-(50)/(x)=10`

Now, we solve for
`x`

`(60x-50x+100)/(x(x-2))=10\\ 10x+100=10x^(2) -20x\\10x^(2) -20x-10x-100=0\\10x^(2)-30x-100=0`

To solve this quadratic equation, we first divide it by 10,

`(10x^(2)-30x-100)/(10) =0\\x^(2) -3x-10=0`

Now, we look for two numbers which product is 10 and which difference is 3,

`x^(2) -3x-10=0\\(x-5)(x+2)=0`

Because, 5 times 2 is 10, and 5 minus 2 is 3.

So, the solutions are

`x=5\\x=-2`

In this case, we are interested only in positive solutions, because the negative one doesn't make sense to the problem.

Finally, we find the time of each person

Jenny:
`x-2=5-2=3`

So, Jenny takes 3 hours.

Maureen:
`x=5`

So, Maureen takes 5 hours.

The speed of each of them,

Jenny:
`s=(60)/(x-2)=(60)/(3) =20mph`

Maureen:
`s=(50)/(x)=(50)/(5)=10mph`.

Answer 2

For the answer to the question above asking Jenny's Speed and Maureen's speed.

The answer to the question is
Jenny's speed is 20 miles per hour
Maureen's speed is 10 miles per hour

I hope my answer helped you. Feel free to ask more questions. Have a nice day!