Question

Two hot air balloons, one purple and one gold, took off at the same time. The purple balloon started from sea level and the gold balloon started from a hill
\[15\] meters above sea level.
The gold balloon began climbing at a constant rate of
\[2\] meters per second. The purple balloon began climbing at
\[2.5\] meters per second.
After how many seconds were the balloons at the same altitude?

Answer 1

Let t be seconds after takeoff. Heights: purple = 2.5t, gold = 15 + 2t. Set equal:

2.5t = 15 + 2t
0.5t = 15
t = 30 seconds.