Amount of time taken for truck over 5.0km

[icesalmon]

Homework Statement

Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 460 Hz; as the truck recedes, you hear a tone of 410 Hz. How much time will it take for the truck to get from your position to the fire 5.0km away, assuming it maintains a constant speed.

Homework Equations

t = Δx/v

The Attempt at a Solution

I'm trying to find the velocity of the truck first so I have 460 = f(340)/(340+v) for the approaching tone, and a receding tone represented by 410 = f(340)/(340-v) and I'm not exactly sure what to do next. Thanks for the help.

 

[rl.bhat]

When the source approaches, the apparent frequency increases. So in the formula for apparent frequency,
denominator should be 340 -v. Write the two formulae and divide to cancel f. Then simplify to get the velocity.