Question

Nour drove from the Dead Sea up to Amman, and her altitude increased at a constant rate. When she began driving, her altitude was 400 meters below sea level. When she arrived in Amman 2 hours later, her altitude was 1000 meters above sea level. Let y represent Nour's altitude (in meters) relative to sea level after x hours. Complete the equation for the relationship between the altitude and number of hours. y=

Answer 1

`\text{y}=700\text{x}-400`

Explanation:

Given: Nour drove from the Dead Sea up to Amman, and her altitude increased at a constant rate. When she began driving, her altitude was
`400` meters below sea level. When she arrived in Amman
`2` hours later, her altitude was
`1000` meters above sea level. Let
`\text{y}` represent Nour's altitude (in meters) relative to sea level after
`\text{x}` hours.

To Find: Complete the equation for the relationship between the altitude and number of hours.
`\text{y}`=.

Solution:

Let the altitude below sea level is represented as negative of altitude and above sea level as positive.

Altitude of Nour when she began driving
`=-400`
`\text{meter}`

Altitude of Nour when she reaches Amman
`=1000`
`\text{meter}`

Time taken to reach Amman from Dead sea
`2`
`\text{hour}`

Altitude changed in
`2`
`\text{hour}`
`=1000-(-400)=1400`
`\text{meter}`

Altitude changed in
`1`
`\text{hour}`
`(1400)/(2)`
`=700`
`\text{meter}`

the altitude gain in
`\text{x}`
`\text{hour}`=
`700\text{x}`
`\text{meter}`

but position of nour at
`0`
`\text{hour}`
`=-400`
`\text{meter}`

Therefore, equation for relationship between the altitude and number of hours is

`\text{y}=700\text{x}-400`