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? seconds

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? seconds

Bytelearn · Accepted Answer

Given Data: We have: Starting altitude of the purple balloon: 0 meters Starting altitude of the gold balloon: 15 meters Rate of climb for the purple balloon: 2.5 meters per second Rate of climb for the gold balloon: 2 meters per second  We need to find the time when the altitude of the purple balloon equals the altitude of the gold balloon.Equation Setup: Let's denote the time in seconds at which the balloons are at the same altitude as t.  The altitude of the purple balloon after t seconds will be: Altitude of purple balloon = 2.5t  The altitude of the gold balloon after t seconds will be: Altitude of gold balloon = 15 + 2t  We set these two expressions equal to each other to find the time when the altitudes are the same: 2.5t = 15 + 2tSolving for t: Now, we solve for t: Subtract 2t from both sides of the equation: 2.5t - 2t = 15 + 2t - 2t 0.5t = 15  Divide both sides by 0.5 to find t: t = 15 / 0.5 t = 30 secondsFinal Result: Therefore, after 30 seconds, the two hot air balloons were at the same altitude.

Full solution

More problems from Solve linear equations with variables on both sides: word problems

Related topics