Question

Noa drove from the Dead Sea up to Jerusalem, and her altitude increased at a constant rate of 740740740 meters per hour. When she arrived in Jerusalem after 1.51.51, point, 5 hours of driving, her altitude was 710710710 meters above sea level. Let AAA represent Noa's altitude (in meters) relative to sea level after ttt hours. Complete the equation for the relationship between the altitude and number of hours.

Answer 1

Answer: The equation for the relationship between the altitude and number of hours is
`A(t)=740t-400`

Explanation:

Since we have given that

Speed = 740 m/hour

Number of hours = 1.5 hours

Let t be the number of hours.

A be the altitude relative to sea level.

So, According to question, it becomes,

`A(t)=740t+x`

where, x is the initial height of Noa.

After 1.5 hours, altitude becomes 710 meters.

`710=740(1.5)+x\\\\710=1110+x\\\\x=1110-710\\\\x=-400\ m`

Hence, the equation for the relationship between the altitude and number of hours is
`A(t)=740t-400`

Answer 2

`A=-400 + 740t`

Explanation:

Let the initial altitude ( in meters ) =
`a_0`,

Since, altitude is increasing at a constant rate of 740 meters per hour.

So, the final altitude ( say A ) in meters after t hours = initial altitude + increment in altitude in t hours,

`\implies A = a_0 + 740t`

According to the question,

A = 710 meters, when t = 1.5 hours,

`710 = a_0 + 740(1.5)`

`710 =a_0 + 1110`

`\implies a_0 = 710 - 1110 = -400`

Hence, the required equation that shows the relationship between the altitude and number of hours,

`A=-400 + 740t`