Firestone Tire & Rubber Co.'s proposed merger with the Borg-Warner Corp. won't take place on the target date of April 24.

In a joint announcement released yesterday, the two companies said they were delaying board and shareholder action on the proposal "because the boards of directors and the management of both companies need more time to complete and analyze the extensive studies needed for a merger of this size."

James F. Bere, chairman and chief executive of Chicago-based Borg-Warner, and Richard A. Riley, his counterpart at the Akron tiremaker, said that progress toward the merger had "been slower than expected."

Studies being prepared to provide the basis for the final agreement are going slowly, they said. Both men, however, emphasized that merger preparations are continuing.

The companies announced plans to merge last Nov. 29, and went as far as to say at that time that a new holding company would be formed to run the operations of the two corporations.

Although that new holding company would have its headquarters in Chicago, the two entities would be run as separate operations, they said. Riley would be chairman and Bere would be president and chief executive officer.

But the first sign of trouble came at the Firestone stockholders meeting a month ago in Akron. At that meeting, an estimated 900 shareholders showed up to question Riley about the tersm of the merger.

Many of those shareholders were unhappy with the offer, which would give them a $16 debenture for each share of Firestone stock held. Many said they had paid as much s $55 a share for their Firestone stock.