If a second car leaves later at a higher speed, how long will it take to catch up?

Question

If a Skoda sets off at an average speed of 20 miles per hour at 7 am and a Porsche sets off at an average speed of 40 miles per hour at 4 pm in the same direction, at what time will the Porsche catch the Skoda?

Could you please explain how it works?

Answer 1

From $7$ am to $4$ pm the Skoda would have travelled $180$ miles. Thus the Porsche has to cover $180$ miles extra to overtake the Skoda. In each hour the Porsche can only cover $20$ miles extra, so the Porsche would need another extra $9$ hours to do that, thus finishing at $1$ am.

Answer 2

Let's say Ds = distance traveled by the Skoda and Dp = distance traveled by the Porsche. If we set t to be the time after 4pm that the cars are traveling, then we set up the formulas as follows:

Dp = 40t Ds = 20t + 20(9) *the Skoda has been travelling from 7am to 4pm, or 9 hours.

When the cars meet, the distance traveled should be the same.

40t = 20t + 180

Subtract 20t from both sides: 20t = 180

Divide both sides by 20: t = 9

So, after 4pm, the Porsche should catch up with the Skoda 9 hours later, or at 1 am.

Answer 3

If you are geometrically inclined, like I am, you can visualize the path of the Skoda as a line on a graph where the X axis is the time of day (in military time) and the Y axis is distance traveled in miles.

Here are some points for the Skoda --

• (7,0), because at 7 am, the Skoda has traveled 0 miles.
• (8,20), because at 8 am, the Skoda has traveled 20 miles.
• (12,100), because at 12 pm, the Skoda has traveled 100 miles.

If you plot these points on your graph, you'll see that it makes a straight line with slope 20 and X-intercept of 7. From that you could figure out that the Y intercept is -140.

Similarly, the Porsche would have a slope of 40 and an X-intercept of 16 (we're using military time). From there you could find out that the Y intercept is -640.

So you have

• Skoda's traveled distance = $20*t - 140$
• Porsche traveled distance = $40*t - 640$

We can graph these on a chart --

So you want to know when their traveled distance is equal. So --

$Skoda \, distance = Porsche \, distance$

$20*t - 140 = 40*t - 640$

$20*t = 40*t - 500$

$20*t = 500$

$t = 25$

So, at 25 o' clock, or 1 am the next day, their traveled distances will be the same.

Answer 4

HINT $\: $ The Porsche travels $\rm 20\ t$ more miles than the Skoda during the time $\rm\:t\:$ they're both driving. This must be equal to the $\ 20\cdot 9$ miles of the Skoda's head start. $\ $ Hence $\rm\ t\ =\ \ldots$

Answer 5

Hint: Distance covered is speed$\times$ time traveled. If you assume the time at which the Skoda leaves to be $t=0$, distance covered by Skoda after $t$ hours is $20t$ and distance covered by Porsche after 4pm is $40(t-9)$.