Question

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

Explanation:

Step1: Define distance functions

Let $t$ = time in seconds.
Terrier distance to ball: $d_1(t) = 90 - 11t$
Greyhound distance to ball: $d_2(t) = 140 - 19t$

Step2: Set distances equal

$$90 - 11t = 140 - 19t$$

Step3: Solve for t

$$19t -11t = 140 -90$$
$$8t = 50$$
$$t = \frac{50}{8} = \frac{25}{4}$$

Answer:

$\frac{25}{4}$ or $6.25$ seconds