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=?

Answer 1

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.

Complete step-by-step answer:
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).