Word Problem: Bus Driver

[Victor30]

A bus driver planned a 2 day trip. He traveled 260km at a certain speed on the first day. He traveled 58 km on the second day but because of weather conditions he reduced his speed by 7km/h. The total time for the trip was 5 hours. How fast did he travel the first day?

 

[soroban]

Hello, Victor30!

A bus driver planned a two-day trip. .He traveled 260 km at a certain speed on the first day.
He traveled 58 km on the second day but because of weather conditions he reduced his speed by 7 km/hr.
The total time for the trip was 5 hours. .How fast did he travel the first day?

The first day, he drove 260 km at \(\displaystyle x\) km/hr.
. . This took: .\(\displaystyle \dfrac{260}{x}\) hours.

The second day, he drove 58 km at \(\displaystyle x-7\) km/hr.
. . This took:\(\displaystyle \dfrac{58}{x-7}\) hours.

Total time is 5 hours: .\(\displaystyle \dfrac{260}{x} + \dfrac{58}{x-7} \:=\:5\)
. . Solve for \(\displaystyle x.\)


Note: this results in a quadratic equation with two roots,
. . . . .but only one is usable.

 

[Victor30]

Thanks Soroban

I struggled with this for several hours. You laid it out very nice and it really make sense. Well done....thanks!