Question

a car is traveling on a small highway and it's either going 55 miles per hour or 35 miles per hour depending on the speed limit until it reaches its destination 200 miles away. Letting X represent the amount of time and hours at the car is going 55 miles per hour and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=2001. if the car spends 2.5 hours going 35 miles per hour on the trip, about how long does it spend going 55 miles per hour? round to the nearest hundereth 2. if the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles an hour3. if the car spends no time going 35 miles per hour, about how long would the trip take? round to the nearest hundereth, why is this?

Answer 1

The relationship equation is,

`55x+35y=200`

(1)

Substitute 2.5 for y in the equation to obtain the value of x.

`\begin{gathered} 55x+35\cdot3.5=200 \\ 55x+122.5=200 \\ x=(77.5)/(55) \\ =1.41 \end{gathered}`

So car travell for 1.41 hours at speed of 55 miles per hour.

(2)

Substitute 3 for x in the equation to obtain the value of y.

`\begin{gathered} 55\cdot3+35y=200 \\ 35y=200-165 \\ y=(35)/(35) \\ =1 \end{gathered}`

So car travell for 1 hour at speed of 35 miles per hour.

(3)

Substitute 0 for y in the equation to obtain the value of x.

`\begin{gathered} 55x+35\cdot0=200 \\ x=(200)/(55) \\ =3.64 \end{gathered}`

So car tarvell for 3.64 hours at the speed of 55 miles per hour.

As the car does not travell any distance at the speed of 35 miles per hour, so time for which car travell at speed of 55 miles per hour is equal to the time taken by car to complete the trip.