In consideration of $1,800 paid to him by Joyce, Hill gave Joyce a written option to purchase

Question:

In consideration of $1,800 paid to him by Joyce, Hill gave Joyce a written option to purchase his house for $180,000 on or before April 1. Prior to April 1, Hill verbally agreed to extend the option until July 1. On May 18, Hill, known to Joyce, sold the house to Gray, who was ignorant of the unrecorded option. On May 20 Joyce sent an acceptance to Hill who received it on May 25. Is there a contract between Joyce and Hill? Explain.