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

By definition, we have to:

$t = \frac{d}{v}$

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:

$t=\frac{154}{v} +\frac{35}{\frac{v}{2}}$

From here, we clear v.

We have then:

$t=\frac{154}{v} +\frac{70}{v}$

$v=\frac{154}{t} +\frac{70}{t}$

Substituting values we have:

$v=\frac{154}{4} +\frac{70}{4}$

$v=56$

Answer:

Grace drives at a rate of 56 miles per hour.

Answer 2

Answer:

56

Step-by-step explanation: