tom was playing fetch in the park with his jack russell terrier. on one throw, the ball landed 90 meters…

tom was playing fetch in the park with his jack russell terrier. on one throw, the ball landed 90 meters from the terrier, and the terrier started running toward it at 11 meters per second. at the same time, a greyhound that was 140 meters away from the ball started running toward it at a speed of 19 meters per second. if each dog kept a constant speed, how long did it take for both dogs to be the same distance from the ball? simplify any fractions. seconds

tom was playing fetch in the park with his jack russell terrier. on one throw, the ball landed 90 meters from the terrier, and the terrier started running toward it at 11 meters per second. at the same time, a greyhound that was 140 meters away from the ball started running toward it at a speed of 19 meters per second. if each dog kept a constant speed, how long did it take for both dogs to be the same distance from the ball? simplify any fractions. seconds

Answer

Explanation:

Step1: Set up distance - time equations

Let $t$ be the time in seconds. The distance of the Jack - Russell terrier from the ball after time $t$ is $d_1=90 - 11t$. The distance of the greyhound from the ball after time $t$ is $d_2 = 140-19t$.

Step2: Set the two distances equal

We want to find when $d_1=d_2$. So, we set up the equation $90 - 11t=140-19t$.

Step3: Solve the equation for $t$

First, add $19t$ to both sides of the equation: $90 - 11t+19t=140-19t + 19t$, which simplifies to $90 + 8t=140$. Then subtract 90 from both sides: $90-90 + 8t=140 - 90$, giving $8t = 50$. Finally, divide both sides by 8: $t=\frac{50}{8}=\frac{25}{4}=6.25$.

Answer:

$\frac{25}{4}$