Question

Robot A:
Distance from base = 30 m
Speed = $\frac{5}{3}$ m/s

Robot B:
Distance from base = 85 m
Speed = $\frac{3}{4}$ m/s

From the data above, find when will Robot A meet Robot B.

• A. 45 seconds
• B. 60 seconds
• C. 72 seconds
• D. 90 seconds

Answer 1

The correct option is B 60 seconds

Given:
For Robot A,
Distance = 30 m
Speed = $\frac{5}{3}$ m/s

For Robot B,
Distance = 85 m
Speed = $\frac{3}{4}$ m/s

Let the time taken for both to meet be $t$ seconds.

Distance covered by Robot A in $t$ seconds = $\frac{5}{3}$$t$
Total distance = $\frac{5}{3}$$t$ + 30

Similarly,
Distance covered by Robot B in $t$ seconds = $\frac{3}{4}$$t$
Total distance = $\frac{3}{4}$$t$ + 85

Since both the robots will meet after $t$ seconds, their distances from the base are equal, i.e.,
$\frac{5}{3}$$t$ + 30 = $\frac{3}{4}$$t$ + 85

$\Rightarrow$ $\frac{5}{3}$$t$ + 30 + (-$\frac{3}{4}$$t$ ) + (-85) = 0
[by commutative property]

$\Rightarrow$ {$\frac{5}{3}$$t$ + (-$\frac{3}{4}$$t$ )} + {30 + (-85)} = 0
[by associative property]

$\Rightarrow$ ($\frac{20-9}{12}$$t$ ) + (-55) = 0

$\Rightarrow$ ($\frac{11}{12}$$t$ ) = 55

$\Rightarrow$ $t$ = 60

Therefore, option (b) is the correct answer.