Two Radio Antennas Are $10 \mathrm {~km}$ Apart on a North-South Axis on High Mountain Tops at North-South

Two radio antennas are $10 \mathrm {~km}$ apart on a north-south axis on high mountain tops at the seacoast. The antennas broadcast identical AM radio signals, in phase, at a frequency of $4.70 \mathrm { MHz }$ . A steamship, $200 \mathrm {~km}$ offshore, travels toward the north at $15 \mathrm {~km} / \mathrm { h }$ and passes east of the antennas. A radio on board the ship is tuned to the broadcast frequency. The reception of the radio signal on the ship is a maximum at a given instant. How much later until the next occurrence of maximum reception? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A) $6.4 \mathrm {~min}$
B) $7.7 \mathrm {~min}$
C) $3.8 \mathrm {~min}$
D) $8.9 \mathrm {~min}$
E) $5.1 \mathrm {~min}$