Question on speed.

Question

Speed of a bus is 45 km/h. If it stops for a few minutes in an hour then its average speed becomes 42 km/h. Find out the time duration it stops for in an hour.

My attempt:

Let Distance be D.

Let the time duration for which it halts be x.

$45=\frac{D}{1}$

$42=\frac{D}{1+x}$

Therefore,

$45=42+42x$

$x=4\frac{2}{7} minuites$

What have I done wrong?

Answer 1

The bus is travelling at 45 mph for $1-x$ hours and is stopped for $x$ hours.

So if it travels a distance $D$ miles then:

$45 = \frac{D}{1-x}$

$42 = \frac{D}{1}$

$\Rightarrow 45 - 45x = 42$

$\Rightarrow x = \frac{45-42}{45} = \frac{3}{45} = \frac{1}{15}$

$x$ measures the stopped time in hours, and we want it in minutes. But the conversion is simple:

$\frac{1}{15} \text{ hours} = \frac{60}{15} \text{ minutes} = 4 \text{ minutes}$

Your answer would be correct if the bus travelled at 45 mph for one hour and then stopped for $x$ minutes until its average speed was 42 mph. But the questions asks how long it is stopped for out of a total time of 1 hour.

Answer 2

What you have done wrong here is that the speed (kilometers per hour) is in hour, while you are calculating $x$ in minutes.

The speed $45$ km/h means that each hour ($60$ minutes) the bus travels $45$km or $45000$m, so each minute the bus travels $750$m.

If it stops for $x$ minutes then in one hour, in terms of $x$, the bus will only travel $45000-750x$ meters, so $45000-750x=42000 \Rightarrow x=4.$

Answer 3

Let us denote by $\tau$ the duration of the break each hour in hours. The average speed over one hour reads $$ V = 0\, \tau + 45\, (1-\tau) = 42\, . $$ Therefore, $\tau = 1-\frac{42}{45} = \frac{1}{15}$ of an hour, which just needs to be converted into minutes. The break lasts $\frac{60}{15} = 4$ minutes.

Answer 4

What you have done is that you found out the duration for which the bus stops in 1 hour and 30/7 minutes. Multiply this by (420/7)/(450/7) .. (ie 1 hour in mintues divided by your time in minutes) and you should get the duration for which it halts in one hour.

Answer 5

While there have been several answers posted already, I think that this approach is a bit more intuitive:

Every hour, the bus travels 42 miles. But its full speed is 45 m/hr. So it's traveling at 42/45 of its full speed. Which means that it's driving only 42/45 of the time, and is stopped the rest of the time. So the portion of time that it's stopped is $1-\frac{42}{45} = \frac{45}{45}-\frac{42}{45} =\frac{3}{45} = \frac{1}{15}$, and one fifteenth of an hour is 4 minutes.

Answer 6

Consider a period of one hour. Lets say bus was moving for x hours and stopped for 1-x hours. when bus was moving, it was moving at speed of 45 mph, so it must have covered 45.x miles, which we know is 42 miles, so

45.x = 42

x = 14/15

1 - x = 1/15

so bus was stationary for 1/15 hours or 4 minutes.

Answer 7

When you say it travels at 45 km/h, you mean that in 60 minutes it goes 45km.

When you say its average speed (over an hour I guess) is 42km/h, you mean that in 60 minutes it goes 42km.

So the bus is travelling at 45 km/h but only travels 42km. How much of an hour does it take to cover 42km if you drive at 45km/h? 42 / 45ths of an hour, or 42/45 x 60 minutes, which is 56 minutes. So it drives at 45km/h for 56 minutes, covering 42km, then stops for 4 minutes (the rest of the hour) going nowhere.