Question

Grace is traveling to an island for vacation. She drives from home at a constant rate for the first 154 miles, then takes a ferry to travel the last 35 miles from the coast to the island. The ferry travels at a constant rate that is half the rate at which Grace drives. Given that the entire trip takes 4 hours, complete the statement below. Grace drives at a rate of miles per hour.

Answer 1

56

Explanation:

Answer 2

By definition, we have to:

`image`

Where,

t: time

d: distance

v: speed

Let's define the following variable:

v: Grace's speed

We write the equation that models the problem:

`t=(154)/(v) +(35)/((v)/(2))`

From here, we clear v.

We have then:

`t=(154)/(v) +(70)/(v)`

`v=(154)/(t) +(70)/(t)`

Substituting values we have:

`v=(154)/(4) +(70)/(4)`

`v=56`

Answer:

Grace drives at a rate of 56 miles per hour.