Solving Linear equations

Question

a small, private plane can fly 400 miles in the same amount of time a jet can fly 1000 miles. If the jet’s speed is 300mph more than the speed of the small plane, find the speeds of both planes

Can anyone help solve this problem.

Answer 1

No need for any equations.

In the "amount of time" mentioned, the jet flies 600 miles further than the other. Since the jet is 300mph faster, the amount of time is... and the speeds are...

See if you can finish the problem.

Answer 2

The distance travelled is proportional to the speed since $d = vt$.

Let $d_1$ represent the distance travelled by the small plane; let $v_1$ denote its speed. Let $d_2$ denote the distance travelled by the jet; let $v_2$ denote its speed. Since the small plane travels $400$ miles in the same amount of time that the jet flies $1000$ miles,

$$\frac{d_1}{d_2} = \frac{v_1t}{v_2t} = \frac{v_1}{v_2} = \frac{400~\text{miles}}{1000~\text{miles}} = \frac{2}{5}$$

Moreover, we know that $v_2 = v_1 + 300~\text{mph}$. Thus,

$$\frac{v_1}{v_2} = \frac{v_1}{v_1 + 300~\text{mph}} = \frac{2}{5}$$

Solve the equation $$\frac{v_1}{v_1 + 300~\text{mph}} = \frac{2}{5}$$ for $v_1$, then substitute your result into the equation $v_2 = v_1 + 300~\text{mph}$ to solve for $v_2$.