Question

Nora’s robot starts 1 foot above the ground and climbs 20 inches every 45 seconds. Henry’s robot starts 2 feet above the ground and climbs 10 inches every 30 seconds. After how many seconds will the robots reach the same height.

Answer 1

To find out when the two robots will reach the same height, we need to set up equations for their respective heights as a function of time.

Let \( N(t) \) be the height of Nora's robot after \( t \) seconds, and \( H(t) \) be the height of Henry's robot after \( t \) seconds.

For Nora's robot:
\[ N(t) = 12 + \frac{40}{9}t \]

For Henry's robot:
\[ H(t) = 24 + \frac{20}{3}t \]

Now, to find when they are at the same height, set \( N(t) = H(t) \) and solve for \( t \):
\[ 12 + \frac{40}{9}t = 24 + \frac{20}{3}t \]

Solve for \( t \), and you'll find the time at which both robots are at the same height.

Answer 2

The answer is 5 I hope this helps