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.
