# Time, Speed and Distance: Arithmetic

The Speed of a Car during the second hour of its Journey is thrice that in the first hour. Also, its third hour's speed is the average speed of the first two hours. Had the car travelled at the second hour speed during all the first three hours, then it would have travelled 150 km more. Find the percentage reduction in time in the second case for the first three hours.

I have found out the speed of the first, second and third hour to be 50,150 and 100 km/h respectively.

However, I am not able to understand what the question has asked for.

It has asked for the percentage reduction in time at the same time it has mentioned 'for first three hours'! Is the question incorrect?

If the question is incorrect, please check if the values of speed that I have found out for the first, second and third hour is correct or not. Thanks.

• @RobbieVanDerzee Can you please explain what they have meant by percentage reduction in time.....percentage reduction w.r.t what? Earlier time under consideration was 3 hours now also the time under consideration is 3 hours. So, how can we find out the % reduction in time? Commented May 10, 2018 at 16:05
• You need to calculate the time for the first case and the second case and compare. Did you do it?
– Moti
Commented May 10, 2018 at 16:38
• I do not think that the 150 distance is required. (1/6-1/9)/(1/6)*100.
– Moti
Commented May 10, 2018 at 16:42

Suppose the three speeds are $V_1,V_2,V_3$ km/hour

You know from the question $$V_2=3V_1$$ and $$V_3=\dfrac{V_1+V_2}{2}$$

The distances travelled in the $3$ hours are $V_1,V_2,V_3$ km, a total of $V_1+ V_2+ V_3$ km

You know from the question $$3V_2 = V_1+ V_2+ V_3 + 150$$

You can solve three equations in three unknowns and, as you say, this gives $V_1=50,V_2=150,V_3=100$ km/hour

The total distance travelled in $3$ hours is $V_1+ V_2+ V_3=300$ km, which would have only taken $2$ hours travelling at $V_2=150$ km/hour, and $2$ hours is about a $33.33 \%$ reduction on $3$ hours

As Moti has said in comments, you do not strictly need the information about $150$ km to find the reduction in time

You can say from the first two equations that $$V_1+ V_2+ V_3 = 2V_2$$ so the journey that takes $3$ hours would have taken $2$ hours at speed $V_2$, a reduction of a third