The Smiths and the Johnsons were competing in the final

leg of the Amazing Race. In their race to the finish, the

Smiths immediately took off on a 165 kilometer path

traveling at an average speed of v kilometers per hour.

The Johnsons' start was delayed by 5 hour. Eventually,

they took a 180 kilometer path to the finish, traveling at

an average speed that was 20 kilometers per hour faster

than the Smiths' speed.

The Johnsons arrived at the finish line first and won the

race!

Question:

The Smiths and the Johnsons were the remaining two pairs in the final leg of the Amazing Race. The Smiths took a path that is only 165 kilometers, but it was bumpy so they couldn't drive very fast. The Johnsons were delayed by 1/2 hour, and then they took a path 180 kilometers long. Lucky for them, they could drive 20 kilometers per hour faster than the Smiths, and so they won. Write an inequality that models the speed at which the Smiths were driving. Use v to represent their speed (in kilometers per hour). Solve the inequality.

Answer:

The velocity of Smiths, v is less than 60 km/hr

Step-by-step explanation:

Here we have

Speed at which Smiths was travelling = v

Distance of travel path of Smiths = 165 m

Speed at which Johnson's was travelling = v + 20

Distance of travel path of Johnson's = 180 m

Time of departure of Johnson's = 0.5 + t

Therefore, since Johnson's won the race, we have;

165/v > 180 / (v + 20) + 0.5

165/v - 180 / (v + 20) > 0.5

3300 - 15·v > (v² + 20·v) * 0.5

- (0.5·v² + 25·v - 3300) > 0

(0.5·v² + 25·v - 3300) < 0

Factorizing, we have;

(v+110) (v-60) < 0

Therefore, v < 60 km/h or v < - 110 km/h

We take the positive value as we are calculating the velocity

Hence the velocity of Smiths, v < 60 km/hr.