Question

Randy drove 540 miles in three times the time it took Andy to travel 135 miles Andy’s speed was slower than Randy’s by 15 miles per hour what were the rate and time of each?

I really need help please!!!

Answer 1

Let's assume

Randy's speed =x mph

we have

Andy’s speed was slower than Randy’s by 15 miles per hour

so,

Andy's speed =x-15

Randy drove 540 miles

so, we can find time taken by Randy

time = distance / speed

so, we get

$t_R=\frac{540}{x}$

we can find time taken by Andy

time = distance / speed

so, we get

$t_A=\frac{135}{x-15}$

Randy drove 540 miles in three times the time it took Andy to travel 135 miles

so,

$t_R=3t_A$

we can plug it

$\frac{540}{x}=3*\frac{135}{x-15}$

now, we can solve for x

$540\left(x-15\right)=405x$

$135x=8100$

$x=60$

so,

Calculation of rate:

Randy's speed is 60 mph

Andy's speed =x-15

Andy's speed =60-15=45mph

Calculation of time:

Randy's time is

$t_R=\frac{540}{x}$

$t_R=\frac{540}{60}$

$t_R=9 hours$

Andy's time is

$t_A=\frac{135}{x-15}$

$t_A=\frac{135}{60-15}$

$t_A=3 hours$