Question

Two jets leave harrisburg at the same time, one flying east at a speed of 20 km/h greater than the other, which is flying west. After 4 h, the planes are 6000 km apart. Find their speeds. A tourist bus leaves Richmond at 1:90 PM for New York City. Exactly 24 minutes later, a truck sets out in the same direction. The tourist bus moved at a steady 60 km/h. The truck travels at 80 km/h. How long does it take the truck to overtake the tour bus?

Answer 1

We know that two jets leave Harrisburg at the same, time, one flying east, and another flying west.

We will denote the speed of the second jet by x (in km/h). Thus, the speed of the first jet is x+20. Remembering that:

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

where v is speed, d is distance and t is time, we know that for the first jet:

$x+20=\frac{d_1}{4}\Rightarrow4x+80=d_1$

Where d₁ represents the distance of the first jet from the starting point. For the second jet:

$x=\frac{d_2}{4}\Rightarrow4x=d_2$

Where d₂ represents the distance of the second jet from the starting point.

We also know that:

$d_1+d_2=6000$

As:

Thus, we have that:

$\begin{gathered} (4x+80)+(4x)=6000 \\ \text{And solving for x, we get:} \\ 8x+80=6000 \\ 8x=5920 \\ x=\frac{5920}{8}=740 \end{gathered}$

This means that the second jet has a speed of 740km/h, and the first jet has a speed of 760km/h (20km/h greater than the second one).