QUESTION

# Vidushi drives at 50 km/hr and starts his journey at 4: 00 am. Vidhu drives at 60 km/hr and starts her journey at 5: 30 am and follows Vidushi. If Vidhu catches Vidushi at ab: cd pm, then a+b+c+d=?

Hint: To solve this problem, we will use the relation between speed, distance and time given by $\text{Speed = }\dfrac{Dis\tan ce}{time}$. We will use this formula along with the conditions mentioned in the question regarding the speed of Vidushi, Vidhu and their starting duration. We will then use the variable t to denote the time it takes Vidhu to catch Vidushi and then solve the problem.

We will first start the problem by understanding the given problem by converting this problem into mathematical formulas. Since Vidhu starts at 5: 30 am, we find the distance covered by Vidushi till that time. Thus, from 4: 00 am to 5: 30 am, Vidushi travels for 90 minutes = 1.5 hours. Thus, using
Distance = Speed $\times$ time
Distance = 50 $\times$ 1.5
Distance = 75 km
Thus, Vidushi is ahead by 75 km at 5: 30 am. Now, let Vidhu catch Vidushi after time t. Thus, we have,
60t = 50t + 75 (Since, Vidushi is ahead by 75 km, so we equate the distances travelled before Vidhu catches up)
10t = 75
t = 7.5 hours
Thus, they meet after 7.5 hours, starting from 5: 30 am. Thus, the time they meet is at 1: 00 pm. We can represent this as 01: 00 pm. Thus, to find a+b+c+d = 0+1+0+0 = 1.
Hence, the correct answer is 1.

Note: Another alternative way to solve this problem is by using the concept of relative motion. In this case, we calculate the relative speed which is 60 – 50= 10 km/hr. Now, the relative distance is 75 km (as calculated in the problem). Thus, using Distance = Speed $\times$ time, we have,
75 = 10 $\times$ time (here, since, we use relative motion, we use relative speed)
Time = 7.5 hours (which is the same as the above problem, now we can solve to get the time of the day, they will reach).