Question

On their 1200 kilometer trip to Texas, the Hiltons first took a train and later a plane. The train, traveling at 48 km/hour, took 2 hours longer than the plane, traveling 240 km/h. How long did the whole trip take?

Answer 1

Answer:

The whole trip took $9\frac{2}{3} \ hours$.

Step-by-step explanation:

For Uniform Motion in a Straight Line:

$\boxed{distance\ (s)=velocity\ (v)\times time\ (t)}$

Given:

total distance (s) = 1200 km

train's velocity ($v_t$) = 48 km/h

plane's velocity ($v_p$) = 240 km/h

train's time ($t_t$) = plane's time ($t_p$) + 2 hours

Let:

train's distance ($s_t$) = x km

Then:

plane's distance ($s_p$) = total distance - train's distance

                                 = (1200 - x) km

$s_t=v_t\times t_t$

$x=48t_t$

$t_t=\frac{x}{48} \ hours$ ... [1]

$s_p=v_p\times t_p$

$1200-x=240t_p$

$t_p=\frac{1200-x}{240} \ hours$ ... [2]

$t_t =t_p+2$

$\frac{x}{48}=\frac{1200-x}{240}+2$

$\frac{5x}{240}=\frac{1200-x}{240}+2$

$2=\frac{5x-(1200-x)}{240}$

$2\times240=6x-1200$

$6x=480+1200$

$x=280\ km$

[1]

$t_t=\frac{x}{48}$

   $=\frac{280}{48}$

   $=5\frac{5}{6} \ hours$

[2]

$t_p=\frac{1200-x}{240}$

   $=\frac{1200-280}{240}$

   $=3\frac{5}{6} \ hours$

$total\ time=t_t+t_p$

                $=5\frac{5}{6} +3\frac{5}{6}$

                $=9\frac{2}{3} \ hours$