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.)

Speed is defined by: , which in this case is

Her speed would be

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

Now, we solve for

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

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

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

So, the solutions are

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:

So, Jenny takes 3 hours.

Maureen:

So, Maureen takes 5 hours.

The speed of each of them,

Jenny:

Maureen: .