The distance between A and B is $330$ km. At 6 am a truck travels from A to B. At a distance of $150$ km from B the truck met a bus that went out from B to A at $7$ am. Find the velocity of the truck if it's smaller by 15 km/h from the velocity of the bus.

This should be so simple but I got stuck and didn't get a correct answer.

So I tried to build a table of velocity, time and distance. The bus travels one hour less than the truck. In addition, it travels faster. But they travel the same distance at the end.

$$\begin{array}{c|c|c|} & \text{$v$ velocity} & \text{$t$ time} &\text{$d$ distance} \\ \hline \text{Truck} & x & t & 330\\ \hline \text{Bus} & x + 15 & t-1 & 330\\ \hline \end{array}$$

A equation in this case is: $$vt = d$$

However, if I resolve this two equations with two variables I don't get a reasonable answer:

$$xt = 350$$ $$(x+15)(t-1) = 350$$

Any help...?

  • How did you get $d = 350$? – Lothar Narins Mar 1 '16 at 18:19
  • @LotharNarins corrected. $x$ should be 60. – Pichi Wuana Mar 1 '16 at 18:21
up vote 3 down vote accepted

"150 km from B the truck meets a bus...". So in your table the distance that the truck traveled in $t$ is $330 - 150 = 180$ km. Similarly the bus managed to travel $150$km in $t-1$ time. This should give you the desired result $x = 60$.

  • Right... But why are my equations wrong? I understand your approach but I would want to know what's wrong in mine. – Pichi Wuana Mar 1 '16 at 18:56
  • 1
    Your approach regarding velocity and time is right, however you assume that with this time assumption and velocity both vehicles travel 330km. – johnnycrab Mar 1 '16 at 19:07
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    But you only know that the bus travels 150km in $t-1$ hours. That doesn't say the bus also needs one hour less to travel the whole 330km than the truck. – johnnycrab Mar 1 '16 at 19:08
  • Oh... right..!! – Pichi Wuana Mar 1 '16 at 19:14

Okay, let's redefine the solution.

Considering truck travel with speed $s$ $km/h$(not velocity as for velocity -ve sign has to be taken through which I was not able to find answer). Therefore bus will travel with Speed $(s+15) km/h$.

As bus and truck met at $150km$ from $B$. Therefore truck has travel $180km$ and bus has travel $150 km$.

Time taken by truck to reach at $180 km$ point be $t$ hr ,then time taken by bus will be $(t-1)$ hr.

So for, truck ,equation will be

$$st = 180 \,\, \Rightarrow \,\, t = (180/s)$$

And for , bus equation will be

$$(t-1)(s+15) = 150$$

Substituting $t =(180/s)$ in equation of bus we get two values of s i.e. $60$ & $45$ .

That means one will be of bus and other will be of truck.

since speed of truck is less than speed of bus by $15 km/hr$.

speed of truck is $45 km/h$ & bus = $60 km/hr$.

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