A slightly different same direction problem

Algebra Level pending

Two sound waves from a point source on the ground travel through the ground to a detector. The speed of one wave is 7.5 km/s, the speed of the other wave is 5.0 km/s. The waves arrive at the detector 15 s apart. What is the distance from the point source to the detector?

113 km 45 km 38 km 225 km

Jonathan Goulding by jonathan goulding , 47, USA

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1 solution

Let D D be the distance (in km) from the point source to the detector. Then with time = distance/speed, the time (in seconds) for the faster wave to reach the detector is D / 7.5 D/7.5 and the time for the slower wave to reach the detector is D / 5 D/5 . Since the waves arrive 15 15 seconds apart, we have that

D 5 − D 7.5 = 15 ⟹ 3 D − 2 D 15 = 15 ⟹ D = 15 × 15 = 225 \dfrac{D}{5} - \dfrac{D}{7.5} = 15 \Longrightarrow \dfrac{3D - 2D}{15} = 15 \Longrightarrow D = 15 \times 15 = \boxed{225} km.

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