Question

Distance of Robot A from base is 48 m and its speed is 2 m/s whereas for Robot B it's 120 m and 2/3 m/s respectively.
Time taken for them to meet is .

• A. 58 seconds
• B. 64 seconds
• C. 54 seconds
• D. 72 seconds

Answer 1

The correct option is C 54 seconds

Given:
For Robot A,
Distance = 48 m
Speed = 2 m/s

For Robot B,
Distance = 120 m
Speed = $\frac{2}{3}$ m/s

Let the time taken for both to meet be $t$ seconds.
So, the distance covered by Robot A in $t$ seconds = 2$t$
Total distance = 2$t$ + 48

Similarly, the distance covered by Robot B in $t$ seconds = $\frac{2}{3}$$t$
Total distance = $\frac{2}{3}$$t$ + 120

Since both the robots meet after $t$ seconds, their distances from the base are equal,
i.e.,

2$t$ + 48 = $\frac{2}{3}$$t$ + 120

$\Rightarrow$ 2$t$ + 48 + (-$\frac{2}{3}$$t$) + (-120) = 0
[by commutative property]

$\Rightarrow$ {2$t$ + (-$\frac{2}{3}$$t$)} + {48 + (-120)} = 0 [Associative property]

$\Rightarrow$ ($\frac{4}{3}$$t$) + (-72) = 0

$\Rightarrow$ ($\frac{4}{3}$$t$) = 72

$\Rightarrow$ $t$ = 54 seconds