Time and speed

Welcome to aptitude tricks
Problems involving Time, Distance and Speed are solved based on one simple formula.
Distance = Speed * Time
Which implies →
Speed = Distance / Time   and
Time = Distance / Speed
Let us take a look at some simple examples of distance, time and speed problems.

Example 1. A boy walks at a speed of 4 kmph. How much time does he take to walk a distance of 20 km?
Solution
Time = Distance / speed = 20/4 = 5 hours.

Example 2. A cyclist covers a distance of 15 miles in 2 hours. Calculate his speed.
Solution
Speed = Distance/time = 15/2 = 7.5 miles per hour.

Example 3. A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?
Solution
Distance covered = 4*40 = 160 miles
Speed required to cover the same distance in 1.5 hours = 160/1.5 = 106.66 mph

Now, take a look at the following example:
Example 4. If a person walks at 4 mph, he covers a certain distance. If he walks at 9 mph, he covers 7.5 miles more. How much distance did he actually cover?
Now we can see that the direct application of our usual formula Distance = Speed * Time or its variations cannot be done in this case and we need to put in extra effort to calculate the given parameters.
Let us see how this question can be solved.
Solution
For these kinds of questions, a table like this might make it easier to solve.
 Distance Speed Time d 4 t d+7.5 9 t

Let the distance covered by that person be ‘d’.
Walking at 4 mph and covering a distance ‘d’ is done in a time of ‘d/4’
IF he walks at 9 mph, he covers 7.5 miles more than the actual distance d, which is ‘d+7.5’.
He does this in a time of (d+7.5)/9.
Since the time is same in both the cases →
d/4 = (d+7.5)/9            →        9d = 4(d+7.5)   →        9d=4d+30        →        d = 6.
So, he covered a distance of 6 miles in 1.5 hours.

Example 5. A train is going at 1/3 of its usual speed and it takes an extra 30 minutes to reach its destination. Find its usual time to cover the same distance.
Solution
Here, we see that the distance is same.
Let us assume that its usual speed is ‘s’ and time is ‘t’, then
 Distance Speed Time d s t min d S+1/3 t+30 min

s*t = (1/3)s*(t+30)      →        t = t/3 + 10      →        t = 15.
So the actual time taken to cover the distance is 15 minutes.
Note: Note the time is expressed in terms of ‘minutes’. When we express distance in terms of miles or kilometers, time is expressed in terms of hours and has to be converted into appropriate units of measurement.

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